A193070 Odd numbers N for which sigma(N^2) is prime.

3, 5, 17, 27, 41, 49, 59, 71, 89, 101, 125, 131, 167, 169, 173, 289, 293, 383, 529, 677, 701, 729, 743, 761, 773, 827, 839, 841, 857, 911, 1091, 1097, 1163, 1181, 1193, 1217, 1373, 1427, 1487, 1559, 1583, 1709, 1811, 1847, 1849, 1931, 1973, 2129, 2197, 2273, 2309

Offset: 1

Author

M. F. Hasler, Jul 15 2011

Keywords

• nonn

Comments

The function sigma(n) (=A000203(n)) takes odd values when n is a square or twice a square. Thus, odd numbers n for which sigma(n) is prime (i.e. which are in A023194) must be odd squares. This sequence consists exactly of the square roots of these terms.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A023194, A195382, A278911.

Programs

Mathematica

Select[Range[1,2401,2],PrimeQ[DivisorSigma[1,#^2]]&] (* Harvey P. Dale, Mar 07 2015 *)

PARI

forstep(N=1, 1e7, 2, isprime(sigma(N^2)) && print1(N", "))

Formula

a(n) = A278911(n)^(1/2). - Robert Israel, Jan 22 2019