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Numbers k such that sigma(k) divides sigma(k!).
1

%I #15 Sep 08 2022 08:46:19

%S 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 32,33,34,35,36,37,38,39,40,41,42,43,44,46,47,49,51,52,53,54,55,56,57,

%U 58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77

%N Numbers k such that sigma(k) divides sigma(k!).

%C 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 Jaroslav Krizek, <a href="/A286758/b286758.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%Y Complement of A262812.

%Y All primes (A000040) are terms.

%Y Cf. A000142, A000203.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, May 14 2017