A065404 Squares of composite numbers k such that sigma(k) (sum of divisors of k, A000203) is a prime.

16, 64, 729, 2401, 4096, 15625, 28561, 65536, 83521, 262144, 279841, 531441, 707281, 3418801, 4826809, 9765625, 24137569, 28398241, 38950081, 47458321, 244140625, 260144641, 887503681, 1073741824, 1387488001, 2655237841

Offset: 1

Author

Labos Elemer, Nov 06 2001

Keywords

• nonn

Examples

			46 cases below 10^12; for M a Mersenne prime, (M+1)/2 is here: M=8191, 4096=(M+1)/2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500 (terms 1..100 from Harry J. Smith)

Crossrefs

Cf. A062700, A000203 (sigma), A065403, A065405, A053182, A053183, A028982.

Programs

PARI

{ n=0; for (m=1, 10^9, if (isprime(m), next); x=sigma(m^2); if (isprime(x), write("b065404.txt", n++, " ", m^2); if (n==100, return)) ) } \\ Harry J. Smith, Oct 18 2009

Formula

sigma(a(n)) = A065403(n).