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

Author

Labos Elemer, Nov 19 2001

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000005 (tau), A000203 (sigma), A065403, A065404, A065405, A028982, A025475.

Programs

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} ]