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

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..11.

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.

Example

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.

Prog

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

Crossrefs

Cf. A076496.

Supersequence of A084306.

Sequence in context: A294156 A108215 A322609 * A228876 A005782 A351379

Adjacent sequences: A234235 A234236 A234237 * A234239 A234240 A234241

Keyword

nonn,more

Author

Michel Marcus, Dec 21 2013

Extensions

a(11) from Donovan Johnson, Dec 23 2013

Status

approved