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

1,1

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000203, A023194, A195382, A278911.

Sequence in context: A256444 A032619 A193066 * A030077 A352568 A058580

Adjacent sequences: A193067 A193068 A193069 * A193071 A193072 A193073

Keyword

nonn

Author

M. F. Hasler, Jul 15 2011

Status

approved