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A369765 Maximal coefficient of (1 + x) * (1 + x^2) * (1 + x^3) * (1 + x^5) * ... * (1 + x^prime(n-1)).

%I A369765 #10 Feb 01 2024 15:00:19
%S A369765 1,1,1,2,2,3,3,6,7,13,19,32,53,90,156,277,494,878,1566,2836,5146,9401,
%T A369765 17358,32042,59434,110292,204332,380548,713601,1342448,2538012,
%U A369765 4808578,9043605,17070234,32268611,61271738,116123939,220993892,421000142,802844420,1534312896
%N A369765 Maximal coefficient of (1 + x) * (1 + x^2) * (1 + x^3) * (1 + x^5) * ... * (1 + x^prime(n-1)).
%t A369765 Table[Max[CoefficientList[Product[(1 + x^If[k == 1, 1, Prime[k - 1]]), {k, 1, n}], x]], {n, 0, 40}]
%o A369765 (Python)
%o A369765 from collections import Counter
%o A369765 from sympy import prime
%o A369765 def A369765(n):
%o A369765     c = {0:1,1:1}
%o A369765     for k in range(1,n):
%o A369765         p, d = prime(k), Counter(c)
%o A369765         for j in c:
%o A369765             d[j+p] += c[j]
%o A369765         c = d
%o A369765     return max(c.values()) # _Chai Wah Wu_, Feb 01 2024
%Y A369765 Cf. A008578, A025591, A036497, A350457, A350514, A369708.
%K A369765 nonn
%O A369765 0,4
%A A369765 _Ilya Gutkovskiy_, Jan 31 2024