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A066112
Numbers n such that sigma_4(n)/sigma_2(n) is an integer but not a prime.
2
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
1,2
LINKS
EXAMPLE
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.
MATHEMATICA
Do[s=DivisorSigma[4, n]; z=DivisorSigma[2, n]; If[IntegerQ[s/z]&&!PrimeQ[s/z], Print[n]], {n, 1, 10000}]
PROG
(PARI) { n=0; for (m=1, 10^9, if (frac(f=sigma(m, 4)/sigma(m, 2)), next); if (!isprime(f), write("b066112.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 01 2010
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 06 2001
EXTENSIONS
Edited by Jon E. Schoenfield, Dec 24 2016
STATUS
approved