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A065772
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Nontrivial prime powers n from A025475 such that tau[n^2] is prime but sigma[n^2] is a composite number.
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1
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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; internal format)
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OFFSET
| 1,1
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FORMULA
| Numbers n such that A000005[A025475(n)^2] is prime but A000203[A025475(n)^2] is composite number.
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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.
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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} ]
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CROSSREFS
| Cf. A000005, A000203, A065403-A065405, A028982, A025475
Sequence in context: A076486 A068529 A096059 * A090333 A137190 A044070
Adjacent sequences: A065769 A065770 A065771 * A065773 A065774 A065775
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Nov 19 2001
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