A369765 Maximal coefficient of (1 + x) * (1 + x^2) * (1 + x^3) * (1 + x^5) * ... * (1 + x^prime(n-1)).
1, 1, 1, 2, 2, 3, 3, 6, 7, 13, 19, 32, 53, 90, 156, 277, 494, 878, 1566, 2836, 5146, 9401, 17358, 32042, 59434, 110292, 204332, 380548, 713601, 1342448, 2538012, 4808578, 9043605, 17070234, 32268611, 61271738, 116123939, 220993892, 421000142, 802844420, 1534312896
Offset: 0
Keywords
Programs
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Mathematica
Table[Max[CoefficientList[Product[(1 + x^If[k == 1, 1, Prime[k - 1]]), {k, 1, n}], x]], {n, 0, 40}] -
Python
from collections import Counter from sympy import prime def A369765(n): c = {0:1,1:1} for k in range(1,n): p, d = prime(k), Counter(c) for j in c: d[j+p] += c[j] c = d return max(c.values()) # Chai Wah Wu, Feb 01 2024