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

0,411

Comments

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

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

Formula

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

Example

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.

Mathematica

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

Prog

(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 */

Crossrefs

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

Sequence in context: A015569 A015329 A276791 * A173860 A123192 A120524

Adjacent sequences: A111897 A111898 A111899 * A111901 A111902 A111903

Keyword

nonn,look

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved