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

%I #10 Feb 01 2024 15:00:19

%S 1,1,1,2,2,3,3,6,7,13,19,32,53,90,156,277,494,878,1566,2836,5146,9401,

%T 17358,32042,59434,110292,204332,380548,713601,1342448,2538012,

%U 4808578,9043605,17070234,32268611,61271738,116123939,220993892,421000142,802844420,1534312896

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

%t Table[Max[CoefficientList[Product[(1 + x^If[k == 1, 1, Prime[k - 1]]), {k, 1, n}], x]], {n, 0, 40}]

%o (Python)

%o from collections import Counter

%o from sympy import prime

%o def A369765(n):

%o c = {0:1,1:1}

%o for k in range(1,n):

%o p, d = prime(k), Counter(c)

%o for j in c:

%o d[j+p] += c[j]

%o c = d

%o return max(c.values()) # _Chai Wah Wu_, Feb 01 2024

%Y Cf. A008578, A025591, A036497, A350457, A350514, A369708.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Jan 31 2024