A084306 Numbers x such that sigma(x) mod x = 12 and x is not divisible by 6. Singular solutions mentioned in A076496.

121, 304, 127744, 33501184, 8589082624

Offset: 1

Author

Labos Elemer, Jun 11 2003

Keywords

• nonn

Comments

If n = P*q, where P is a multiple perfect number and q is prime so that gcd(P,q) = 1, then sigma(n) = kn(q+1). Consequently sigma(n) = knq + kn sigma(n) mod n = kn. Such values of n are regular solutions to this and analogous cases. Here, not these but the additional eccentric solutions are collected. Cf. A076496.

a(6) > 10^11. - Donovan Johnson, Sep 20 2012

If p = 2^k - 13 > 3 is a prime number, then 2^(k-1)*p is a term. This happens for k = 5, 9, 13, 17, 57, 105, 137, 3217, ... (A096818). - Giovanni Resta, Apr 01 2014

Examples

			n = 33501184 = 4096*8179; sigma(n) = 2n + 12 = 67002380.
		

Crossrefs

Cf. A076496, A076495, A000396, A045768-A045770, A007691, A096818.

Programs

Mathematica

Do[s=Mod[DivisorSigma[1, n], n]; If[IntegerQ[n/100000], Print[{n}]]; If[Equal[s, 12]&&!Equal[Mod[n, 6], 0], Print[n]], {n, 1, 100000000}]

Extensions

a(5) from Donovan Johnson, Sep 20 2012