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%I #15 Nov 09 2023 15:09:37
%S 1,4,16,52,157,434,1144,2862,6906,16090,36449,80430,173555,366802,
%T 761102,1552569,3118508,6174461,12064383,23283027,44419855,83834278,
%U 156626605,289839251,531534746,966483534,1743164649,3119864511,5543030861,9779552117,17139055493
%N Euler transform of composite numbers.
%H Robert Israel, <a href="/A197132/b197132.txt">Table of n, a(n) for n = 0..10000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F G.f.: Product_{k>=1} (1-x^k)^-composite(k), where composite(k) = A002808(k) is the k-th composite number.
%p N:= 100: # to use composites <= N
%p comps:= remove(isprime,[$4..N]):
%p M:= nops(comps):
%p G:= mul((1-x^k)^(-comps[k]),k=1..M):
%p S:= series(G, x, M+1):
%p seq(coeff(S,x,j),j=0..M); # _Robert Israel_, Jan 30 2018
%t a[ns_Integer?NonNegative, nf_Integer?NonNegative] := CoefficientList[Series[Product[(1 - x^k)^-FixedPoint[k + PrimePi[#] + 1 &, k], {k, 1, nf}], {x, 0, nf}], x][[ns + 1 ;; nf + 1]]; a[0, 30] (* _Robert P. P. McKone_, Nov 08 2023 *)
%Y Cf. A002808, A030009.
%K nonn
%O 0,2
%A _Franklin T. Adams-Watters_, Oct 10 2011
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