login
A065772
Nontrivial prime powers k from A025475 such that tau(k^2) is prime but sigma(k^2) is a composite number.
2
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
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
Sequence in context: A096059 A326742 A246328 * A305755 A090333 A137190
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 19 2001
STATUS
approved