Definition:Highly Abundant Number/Examples

Examples of Highly Abundant Numbers
The divisor sum values of the first few highly abundant numbers can be tabulated as:


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! align="right" style = "padding: 2px 10px" | $n$ ! align="right" style = "padding: 2px 10px" | $\map {\sigma_1} n$ ! style = "padding: 2px 10px" | Difference from previous peak
 * align="right" style = "padding: 2px 10px" | $1$
 * align="right" style = "padding: 2px 10px" | $1$
 * align="right" style = "padding: 2px 10px" |
 * align="right" style = "padding: 2px 10px" | $2$
 * align="right" style = "padding: 2px 10px" | $3$
 * align="right" style = "padding: 2px 10px" | $2$
 * align="right" style = "padding: 2px 10px" | $3$
 * align="right" style = "padding: 2px 10px" | $4$
 * align="right" style = "padding: 2px 10px" | $1$
 * align="right" style = "padding: 2px 10px" | $4$
 * align="right" style = "padding: 2px 10px" | $7$
 * align="right" style = "padding: 2px 10px" | $3$
 * align="right" style = "padding: 2px 10px" | $6$
 * align="right" style = "padding: 2px 10px" | $12$
 * align="right" style = "padding: 2px 10px" | $5$
 * align="right" style = "padding: 2px 10px" | $8$
 * align="right" style = "padding: 2px 10px" | $15$
 * align="right" style = "padding: 2px 10px" | $3$
 * align="right" style = "padding: 2px 10px" | $10$
 * align="right" style = "padding: 2px 10px" | $18$
 * align="right" style = "padding: 2px 10px" | $3$
 * align="right" style = "padding: 2px 10px" | $12$
 * align="right" style = "padding: 2px 10px" | $28$
 * align="right" style = "padding: 2px 10px" | $10$
 * align="right" style = "padding: 2px 10px" | $16$
 * align="right" style = "padding: 2px 10px" | $31$
 * align="right" style = "padding: 2px 10px" | $3$
 * align="right" style = "padding: 2px 10px" | $18$
 * align="right" style = "padding: 2px 10px" | $39$
 * align="right" style = "padding: 2px 10px" | $8$
 * align="right" style = "padding: 2px 10px" | $20$
 * align="right" style = "padding: 2px 10px" | $42$
 * align="right" style = "padding: 2px 10px" | $3$
 * align="right" style = "padding: 2px 10px" | $24$
 * align="right" style = "padding: 2px 10px" | $60$
 * align="right" style = "padding: 2px 10px" | $18$
 * align="right" style = "padding: 2px 10px" | $30$
 * align="right" style = "padding: 2px 10px" | $72$
 * align="right" style = "padding: 2px 10px" | $12$
 * align="right" style = "padding: 2px 10px" | $36$
 * align="right" style = "padding: 2px 10px" | $91$
 * align="right" style = "padding: 2px 10px" | $19$
 * align="right" style = "padding: 2px 10px" | $42$
 * align="right" style = "padding: 2px 10px" | $96$
 * align="right" style = "padding: 2px 10px" | $5$
 * align="right" style = "padding: 2px 10px" | $48$
 * align="right" style = "padding: 2px 10px" | $124$
 * align="right" style = "padding: 2px 10px" | $28$
 * align="right" style = "padding: 2px 10px" | $60$
 * align="right" style = "padding: 2px 10px" | $168$
 * align="right" style = "padding: 2px 10px" | $44$
 * align="right" style = "padding: 2px 10px" | $72$
 * align="right" style = "padding: 2px 10px" | $195$
 * align="right" style = "padding: 2px 10px" | $27$
 * align="right" style = "padding: 2px 10px" | $84$
 * align="right" style = "padding: 2px 10px" | $224$
 * align="right" style = "padding: 2px 10px" | $29$
 * align="right" style = "padding: 2px 10px" | $90$
 * align="right" style = "padding: 2px 10px" | $234$
 * align="right" style = "padding: 2px 10px" | $10$
 * align="right" style = "padding: 2px 10px" | $96$
 * align="right" style = "padding: 2px 10px" | $252$
 * align="right" style = "padding: 2px 10px" | $18$
 * align="right" style = "padding: 2px 10px" | $108$
 * align="right" style = "padding: 2px 10px" | $280$
 * align="right" style = "padding: 2px 10px" | $28$
 * align="right" style = "padding: 2px 10px" | $120$
 * align="right" style = "padding: 2px 10px" | $360$
 * align="right" style = "padding: 2px 10px" | $80$
 * }
 * align="right" style = "padding: 2px 10px" | $195$
 * align="right" style = "padding: 2px 10px" | $27$
 * align="right" style = "padding: 2px 10px" | $84$
 * align="right" style = "padding: 2px 10px" | $224$
 * align="right" style = "padding: 2px 10px" | $29$
 * align="right" style = "padding: 2px 10px" | $90$
 * align="right" style = "padding: 2px 10px" | $234$
 * align="right" style = "padding: 2px 10px" | $10$
 * align="right" style = "padding: 2px 10px" | $96$
 * align="right" style = "padding: 2px 10px" | $252$
 * align="right" style = "padding: 2px 10px" | $18$
 * align="right" style = "padding: 2px 10px" | $108$
 * align="right" style = "padding: 2px 10px" | $280$
 * align="right" style = "padding: 2px 10px" | $28$
 * align="right" style = "padding: 2px 10px" | $120$
 * align="right" style = "padding: 2px 10px" | $360$
 * align="right" style = "padding: 2px 10px" | $80$
 * }
 * align="right" style = "padding: 2px 10px" | $120$
 * align="right" style = "padding: 2px 10px" | $360$
 * align="right" style = "padding: 2px 10px" | $80$
 * }
 * }

Thus the sequence of peak divisor sums begins:
 * $1, 3, 4, 7, 12, 15, 18, 28, 31, 39, 42, 60, 72, 91, 96, 124, 168, 195, 224, 234, 252, 280, 360, \ldots$