A065771 Prime powers n such that both tau(n^2) and sigma(n^2) are composite numbers.

16, 81, 128, 625, 1024, 2187, 2401, 4096, 8192, 14641, 28561, 59049, 65536, 78125, 83521, 130321, 131072, 279841, 524288, 531441, 707281, 823543, 923521, 1594323, 1874161, 2825761, 3418801, 4194304, 4879681, 7890481, 9765625, 12117361, 13845841, 16777216

Offset: 1

Author

Labos Elemer, Nov 19 2001

Keywords

• nonn

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000203, A065403-A065405, A028982, A025475.

Programs

Mathematica

Do[ s=DivisorSigma[ 0, n^2 ]; y=DivisorSigma[ 1, n^2 ]; If[ Equal[ Length[ FactorInteger[ n ] ], 1 ]&&!PrimeQ[ n ] &&!PrimeQ[ s ]&&!PrimeQ[ y ], Print[ n ] ], {n, 1, 10000000} ]
Select[Range[16778000],PrimePowerQ[#]&&AllTrue[{DivisorSigma[ 0,#^2],DivisorSigma[ 1,#^2]},CompositeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 18 2021 *)

Formula

A000005(A025475(n)^2) and A000203(A025475(n)^2) are composite numbers.