This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A286758 #32 Aug 01 2025 09:25:34 %S A286758 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, %T A286758 32,33,34,35,36,37,38,39,40,41,42,43,44,46,47,49,51,52,53,54,55,56,57, %U A286758 58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77 %N A286758 Numbers k such that sigma(k) divides sigma(k!). %C A286758 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). %H A286758 Paolo Xausa, <a href="/A286758/b286758.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Jaroslav Krizek) %e A286758 8 is a term because sigma(8!) / sigma(8) = sigma(40320) / sigma(8) = 159120 / 15 = 10608 (integer). %t A286758 A286758Q[k_] := PrimeQ[k] || Divisible[DivisorSigma[1, k!], DivisorSigma[1, k]]; %t A286758 Select[Range[100], A286758Q] (* _Paolo Xausa_, Jul 31 2025 *) %o A286758 (Magma) [n: n in [1..100] | (SumOfDivisors(Factorial(n))) mod SumOfDivisors(n) eq 0]; %Y A286758 Complement of A262812. %Y A286758 All primes (A000040) are terms. %Y A286758 Cf. A000142, A000203. %K A286758 nonn %O A286758 1,2 %A A286758 _Jaroslav Krizek_, May 14 2017