

A282289


Expansion of (Sum_{p prime, k>=2} x^(p^k))^4.


1



0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 4, 0, 0, 6, 12, 6, 0, 8, 12, 12, 4, 13, 16, 6, 4, 13, 28, 12, 4, 10, 24, 24, 16, 28, 24, 24, 24, 42, 52, 18, 28, 32, 60, 40, 24, 44, 28, 42, 28, 60, 52, 18, 24, 37, 84, 54, 48, 42, 60, 78, 48, 72, 44, 60, 52, 68, 96, 36, 40, 22, 72, 72, 52, 76, 52, 66, 36, 88, 88, 64, 56
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OFFSET

0,21


COMMENTS

Number of ways to write n as an ordered sum of 4 proper prime powers (A246547).
Conjecture: a(n) > 0 for all n > 27.


LINKS

Table of n, a(n) for n=0..91.
Ilya Gutkovskiy, Extended graphical example
Eric Weisstein's World of Mathematics, Prime Power


FORMULA

G.f.: (Sum_{p prime, k>=2} x^(p^k))^4.


EXAMPLE

a(28) = 8 because we have [16, 4, 4, 4], [8, 8, 8, 4], [8, 8, 4, 8], [8, 4, 8, 8], [4, 16, 4, 4], [4, 8, 8, 8], [4, 4, 16, 4] and [4, 4, 4, 16].


MATHEMATICA

nmax = 91; CoefficientList[Series[Sum[Sign[PrimeOmega[k]  1] Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]^4, {x, 0, nmax}], x]


CROSSREFS

Cf. A246547, A280242, A280243, A282062, A282064.
Sequence in context: A285242 A143266 A133845 * A291696 A291649 A216060
Adjacent sequences: A282286 A282287 A282288 * A282290 A282291 A282292


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Feb 11 2017


STATUS

approved



