78

Number
$78$ (seventy-eight) is:


 * $2 \times 3 \times 13$


 * The $2$nd element of the $1$st set of $4$ positive integers which form an arithmetic sequence which all have the same Euler $\phi$ value:
 * $\map \phi {72} = \map \phi {78} = \map \phi {84} = \map \phi {90} = 24$


 * The $5$th sphenic number after $30$, $42$, $66$, $70$:
 * $78 = 2 \times 3 \times 13$


 * The smallest positive integer which can be expressed as the sum of $2$ odd primes in $7$ ways.


 * The $8$th integer $n$ after $1$, $3$, $15$, $30$, $35$, $56$, $70$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:
 * $\map {\sigma_0} {78} = 8$, $\map \phi {78} = 24$, $\map {\sigma_1} {78} = 168$


 * The $12$th triangular number after $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$, $55$, $66$:
 * $78 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = \dfrac {12 \times \paren {12 + 1} } 2$


 * The $17$th semiperfect number after $6$, $12$, $18$, $20$, $24$, $28$, $30$, $36$, $40$, $42$, $48$, $54$, $56$, $60$, $66$, $72$:
 * $78 = 13 + 26 + 39$


 * The $45$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $55$, $60$, $61$, $65$, $66$, $67$, $72$, $73$, $77$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$

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