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A065772 Nontrivial prime powers n from A025475 such that tau[n^2] is prime but sigma[n^2] is a composite number. 1
9, 25, 32, 121, 243, 343, 361, 961, 1331, 1369, 1681, 2048, 2209, 2809, 3481, 3721, 4489, 5041, 6561, 6859, 7921, 9409, 10201, 10609, 11449, 11881, 12167, 12769, 16384, 16807, 17161, 18769, 19321, 19683, 22201, 22801, 24389, 24649, 26569 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..39.

FORMULA

Numbers n such that A000005[A025475(n)^2] is prime but A000203[A025475(n)^2] is composite number.

EXAMPLE

n=32: tau[1024]=11, sigma[1024]=2047=23.89; n=243, tau[59049]=11, sigma[59049]=88573=23.3851. Up to 10000000, 453 terms were found.

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} ]

CROSSREFS

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

Sequence in context: A096059 A326742 A246328 * A305755 A090333 A137190

Adjacent sequences:  A065769 A065770 A065771 * A065773 A065774 A065775

KEYWORD

nonn

AUTHOR

Labos Elemer, Nov 19 2001

STATUS

approved

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Last modified June 1 09:53 EDT 2020. Contains 334762 sequences. (Running on oeis4.)