Definition:Highly Abundant Number/Examples

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Examples of Highly Abundant Numbers

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

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

Thus the sequence of peak divisor sums begins:

$1, 3, 4, 7, 12, 15, 18, 28, 31, 39, 42, 60, 72, 91, 96, 124, 168, 195, 224, 234, 252, 280, 360, \ldots$

This sequence is A034885 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).