A065771 - OEIS

%I #11 Jan 18 2021 13:22:30

%S 16,81,128,625,1024,2187,2401,4096,8192,14641,28561,59049,65536,78125,

%T 83521,130321,131072,279841,524288,531441,707281,823543,923521,

%U 1594323,1874161,2825761,3418801,4194304,4879681,7890481,9765625,12117361,13845841,16777216

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

%H Donovan Johnson, <a href="/A065771/b065771.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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} ]

%t Select[Range[16778000],PrimePowerQ[#]&&AllTrue[{DivisorSigma[ 0,#^2],DivisorSigma[ 1,#^2]},CompositeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 18 2021 *)

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

%K nonn

%O 1,1

%A _Labos Elemer_, Nov 19 2001