A111900 Number of partitions of n into distinct squares of primes.

1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0

Offset: 0

Author

Reinhard Zumkeller, Aug 20 2005

Keywords

• nonn
• look

Comments

a(n) <= 1 for n < 410.

Examples

			G.f. = 1 + x^4 + x^9 + x^13 + x^25 + x^29 + x^34 + x^38 + x^49 + x^53 + x^58 + x^62 + ...
410 = 7^2 + 19^2 = 11^2 + 17^2, therefore a(410)=2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000
• Alois P. Heinz, Plot of the first 100000 terms
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A090677, A001248, A033461, A106244, A111902, A287965.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Product[1 + x^Prime[k]^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Ilya Gutkovskiy, Jun 15 2017 *)

PARI

{a(n) = if(n < 0, 0, polcoeff( prod(k=1, primepi(sqrtint(n)), 1 + x^prime(k)^2 + x*O(x^n)), n))}; /* Michael Somos, Dec 26 2016 */

Formula

G.f.: Product_{k>=1} (1 + x^(prime(k)^2)). - Ilya Gutkovskiy, Dec 26 2016