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Number of ways to write n as an ordered sum of 6 prime powers (including 1).
8

%I #6 Feb 05 2021 18:44:07

%S 1,6,21,56,126,246,432,702,1077,1576,2232,3072,4118,5382,6891,8638,

%T 10653,12948,15563,18486,21783,25398,29394,33708,38422,43452,49008,

%U 54888,61308,68076,75434,83034,91473,100248,109947,120018,131191,142458,155049,167622,181629,195660

%N Number of ways to write n as an ordered sum of 6 prime powers (including 1).

%p q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:

%p b:= proc(n, t) option remember;

%p `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(

%p `if`(q(j), b(n-j, t-1), 0), j=1..n)))

%p end:

%p a:= n-> b(n, 6):

%p seq(a(n), n=6..47); # _Alois P. Heinz_, Feb 05 2021

%t nmax = 47; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^6, {x, 0, nmax}], x] // Drop[#, 6] &

%Y Cf. A000961, A010055, A282062, A282064, A341124, A341133, A341134, A341136, A341137, A341138, A341139.

%K nonn

%O 6,2

%A _Ilya Gutkovskiy_, Feb 05 2021