A065772 Nontrivial prime powers k from A025475 such that tau(k^2) is prime but sigma(k^2) is a composite number.

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

Offset

1,1

Comments

Numbers k = A025475(m) such that A000005(k^2) is prime but A000203(k^2) is composite number.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

For k = 32: k^2 = 1024, tau(1024) = 11, sigma(1024) = 2047 = 23*89.
For k = 243, k^2 = 59049, 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 (tau), A000203 (sigma), A065403, A065404, A065405, A028982, A025475.

Sequence in context: A096059 A326742 A246328 * A305755 A090333 A137190

Adjacent sequences: A065769 A065770 A065771 * A065773 A065774 A065775

Keyword

nonn,changed

Author

Labos Elemer, Nov 19 2001

Status

approved