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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
OFFSET
0,411
COMMENTS
a(n) <= 1 for n < 410.
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
KEYWORD
nonn,look
AUTHOR
Reinhard Zumkeller, Aug 20 2005
STATUS
approved