A074384 Solutions to mod(sigma(x), 6) = 5.

2401, 9604, 21609, 28561, 38416, 60025, 86436, 114244, 130321, 153664, 194481, 240100, 257049, 290521, 345744, 456976, 521284, 540225, 614656, 693889, 714025, 777924, 923521, 960400, 1028196, 1162084, 1172889, 1270129, 1382976, 1500625

Offset: 1

Author

Labos Elemer, Aug 22 2002

Keywords

• nonn

Examples

			4th powers of primes of the form 6k+1 are here because sigma[p^4]=p^4+p^3+p^2+p+1 congruent 1+1+1+1+1=5 mod 6. There are also other fourth powers, like 38416=(2*7)^4, 194481=(3*7)^4, 456976=(2*13)^4, and solutions which are not fourth powers like 9604=2^2*7^4 and 21609=3^2*7^4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A072862, A072461, A072462.

Programs

Mathematica

Do[s=Mod[DivisorSigma[1, n], 6]; If[s==5, Print[n]], {n, 1, 1000000}]
Select[Range[1600000],Mod[DivisorSigma[1,#],6]==5&] (* Harvey P. Dale, Jul 06 2014 *)

Formula

{n: A084301(n) = 5}. - R. J. Mathar, May 19 2020