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

1,1

Links

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A354799 A359784 A346484 * A320965 A295071 A223951

Adjacent sequences: A065768 A065769 A065770 * A065772 A065773 A065774

Keyword

nonn

Author

Labos Elemer, Nov 19 2001

Status

approved