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A111900 Number of partitions of n into distinct squares of primes. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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: A016049 A015569 A015329 * A173860 A120524 A014177

Adjacent sequences:  A111897 A111898 A111899 * A111901 A111902 A111903

KEYWORD

nonn,look

AUTHOR

Reinhard Zumkeller, Aug 20 2005

STATUS

approved

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Last modified August 14 16:04 EDT 2018. Contains 313751 sequences. (Running on oeis4.)