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 A281477 Expansion of Sum_{k>=1} x^(prime(k)^2)/(1 + x^(prime(k)^2)) * Product_{k>=1} (1 + x^(prime(k)^2)). 1
 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 COMMENTS Total number of parts in all partitions of n into distinct squares of primes (A001248). LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Ilya Gutkovskiy, Extended graphical example FORMULA G.f.: Sum_{k>=1} x^(prime(k)^2)/(1 + x^(prime(k)^2)) * Product_{k>=1} (1 + x^(prime(k)^2)). EXAMPLE a(38) = 3 because we have [25, 9, 4]. MAPLE Primes:= select(isprime, [\$1..20]): g:= add(x^(p^2)/(1+x^(p^2)), p=Primes)*mul(1+x^(p^2), p=Primes): S:= series(g, x, 20^2+1): seq(coeff(S, x, n), n=1..20^2); # Robert Israel, Feb 08 2017 MATHEMATICA nmax = 125; Rest[CoefficientList[Series[Sum[x^Prime[k]^2/(1 + x^Prime[k]^2), {k, 1, nmax}] Product[1 + x^Prime[k]^2, {k, 1, nmax}], {x, 0, nmax}], x]] CROSSREFS Cf. A001248, A024938, A048261, A111900, A121518, A281449, A281542, A281668. Sequence in context: A071164 A027345 A086080 * A070139 A116860 A179391 Adjacent sequences:  A281474 A281475 A281476 * A281478 A281479 A281480 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 27 2017 STATUS approved

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