A234238 Sporadic solutions to sigma(n) == 12 modulo n.

24, 54, 121, 304, 780, 2352, 127744, 430272, 33501184, 184773312, 8589082624

Offset: 1

Author

Michel Marcus, Dec 21 2013

Keywords

• nonn
• more

Comments

Terms of A076496 that are either not divisible by 6 or such that x/6 is not coprime to 6.

10384593717069654320312270165377024 is also a term. - Donovan Johnson, Dec 23 2013

Examples

			sigma(24) % 24 = 12, and 24/6 is not coprime to 6, hence 24 is here.
sigma(121) % 121 = 12, and 121 is not divisible by 6, hence 121 is here.
		

Links

• A. Anavi, P. Pollack, C. Pomerance, On congruences of the form sigma(n) == a (mod n), Int. J. Number Theory 09, 115 (2013).
• P. Pollack, The sum of divisors of n, modulo n, CNTA 2012.

Crossrefs

Cf. A076496.

Supersequence of A084306.

Programs

PARI

a(n) = m = 6; a = sigma(m) ; ((sigma(n) % n) == a) && ((n % m) || (!(n % m) && (gcd(m, (n/m)) != 1)));

Extensions

a(11) from Donovan Johnson, Dec 23 2013