A066112 Numbers k such that sigma_4(k)/sigma_2(k) is an integer but not a prime.

1, 16, 36, 48, 49, 64, 81, 100, 121, 144, 162, 180, 196, 225, 245, 256, 324, 361, 400, 432, 441, 484, 500, 529, 576, 605, 625, 648, 676, 729, 784, 841, 900, 931, 980, 1024, 1089, 1156, 1200, 1225, 1280, 1296, 1369, 1444, 1521, 1600, 1620, 1681, 1764, 1805

Offset: 1

Author

Labos Elemer, Dec 06 2001

Keywords

• nonn

Examples

			The sequence includes squares, twice squares (such as 162 and 648), and other numbers (such as 48 and 180). The sigma_4/sigma_2 quotients usually have more than one distinct prime factor. Exception: sigma_4(48)/sigma_2(48) = 5732210/3410 = 1681 = 41^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

Cf. A001157, A001159, A046871, A066109, A066110, A066111.

Programs

Mathematica

Do[s=DivisorSigma[4, n]; z=DivisorSigma[2, n]; If[IntegerQ[s/z]&&!PrimeQ[s/z], Print[n]], {n, 1, 10000}]

PARI

isok(k) = { my(f=sigma(k, 4)/sigma(k, 2)); !frac(f) && !isprime(f) } \\ Harry J. Smith, Feb 01 2010

Extensions

Edited by Jon E. Schoenfield, Dec 24 2016