A286758 Numbers k such that sigma(k) divides sigma(k!).

1, 2, 3, 5, 7, 8, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset

1,2

Comments

Conjecture: If p is Fermat prime > 3 from A019434 both values sigma((p-1)!) mod sigma(p-1) and sigma(T(p-1)) mod sigma(p-1) are not 0, where T(n) is the n-th triangular number A000217(n) and n! is the factorial number A000142(n).

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000 (first 1000 terms from Jaroslav Krizek)

Example

8 is a term because sigma(8!) / sigma(8) = sigma(40320) / sigma(8) = 159120 / 15 = 10608 (integer).

Mathematica

A286758Q[k_] := PrimeQ[k] || Divisible[DivisorSigma[1, k!], DivisorSigma[1, k]];
Select[Range[100], A286758Q] (* Paolo Xausa, Jul 31 2025 *)

Prog

(Magma) [n: n in [1..100] | (SumOfDivisors(Factorial(n))) mod SumOfDivisors(n) eq 0];

Crossrefs

Complement of A262812.

All primes (A000040) are terms.

Cf. A000142, A000203.

Sequence in context: A194798 A302245 A028728 * A106735 A028743 A082634

Adjacent sequences: A286755 A286756 A286757 * A286759 A286760 A286761

Keyword

nonn

Author

Jaroslav Krizek, May 14 2017

Status

approved