A234238 Sporadic solutions m to the congruence sigma(m) == 12 (mod m).

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

Offset

1,1

Comments

Terms m of A076496 that are either not divisible by 6 (cf. A084306) or such that m/6 is not coprime to 6 (cf. A216697).

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

a(12) > 10^24. - Max Alekseyev, Jan 20 2026

Links

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

Max A. Alekseyev, Computing bounded solutions to linear Diophantine equations with the sum of divisors, arXiv:2601.17832 [math.NT], 2026. See p. 9.

Aria Anavi, Paul Pollack, and Carl Pomerance, On congruences of the form sigma(n) == a (mod n), Int. J. Number Theory 09 (2013), 115-124.

Paul 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

Union of A084306 and A216697.

Cf. A076496.

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