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A065771
Prime powers n such that both tau(n^2) and sigma(n^2) are composite numbers.
2
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
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 *)
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 19 2001
STATUS
approved