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A369775
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Maximal coefficient of (1 + x^2) * (1 + x^2 + x^3) * (1 + x^2 + x^3 + x^5) * ... * (1 + x^2 + ... + x^prime(n)).
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1
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1, 1, 2, 5, 16, 65, 293, 1807, 12946, 106475, 972260, 9858553, 109451903, 1323071345, 17398667717, 247055196932, 3753507625272, 60680317203979, 1043036844360792, 18969267205680868, 364107881070036688, 7366172106829696356, 156467911373737550264
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OFFSET
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0,3
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LINKS
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MATHEMATICA
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Table[Max[CoefficientList[Product[(1 + Sum[x^Prime[j], {j, 1, i}]), {i, 1, n}], x]], {n, 0, 22}]
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PROG
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(PARI) a(n) = vecmax(Vec(prod(k=1, n, 1 + sum(i=1, k, x^prime(i))))); \\ Michel Marcus, Feb 01 2024
(Python)
from collections import Counter
from sympy import prime, primerange
if n == 0: return 1
c, p = {0:1}, list(primerange(prime(n)+1))
for k in range(1, n+1):
d = Counter(c)
for j in c:
a = c[j]
for i in p[:k]:
d[j+i] += a
c = d
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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