A262812 Values of n such that sigma(n!) mod sigma(n) is not 0.

4, 6, 9, 10, 16, 25, 45, 48, 50, 64, 86, 122, 192, 256, 289, 314, 326, 448, 562, 578, 706, 722, 729, 794, 842, 1226, 1346, 1458, 1514, 1681, 1754, 1922, 2186, 2401, 2566, 2601, 2916, 3362, 3481, 3866, 3986, 4046, 4096, 4274, 4852, 5043, 5186, 5414

Offset: 1

Author

Altug Alkan, Oct 03 2015

Keywords

• nonn

Comments

Subsequence of A002808.

Motivation was the investigation of sum of divisors of n! in terms of sum of divisors of n.

Obviously, a(n) cannot be a prime number, although it can be a semiprime number.

Is this sequence infinite?

Examples

			a(1) = 4 because sigma(4!) mod sigma(4) = 60 mod 7 = 4.
a(2) = 6 because sigma(6!) mod sigma(6) = 2418 mod 12 = 6.
a(3) = 9 because sigma(9!) mod sigma(9) = 1481040 mod 13 = 2.
		

Crossrefs

Cf. A062569, A000203.

Programs

PARI

for(n=1, 1e30, if( sigma(n!) % sigma(n) != 0 , print1(n", ")))

Formula

A066247(a(n)) = 1.

A000005(a(n)) > 2.

A001222(a(n)) > 1.