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A369708
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Maximal coefficient of (1 + x^3) * (1 + x^5) * (1 + x^7) * ... * (1 + x^prime(n)).
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2
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1, 1, 1, 1, 1, 1, 2, 2, 4, 5, 8, 14, 23, 40, 70, 126, 221, 394, 711, 1290, 2354, 4344, 8015, 14868, 27585, 51094, 95160, 178436, 335645, 634568, 1202236, 2261052, 4267640, 8067296, 15318171, 29031484, 55248527, 105251904, 200711160, 383580180, 733704990
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OFFSET
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0,7
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LINKS
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MAPLE
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b:= proc(n) option remember; `if`(n<2, 1, expand(b(n-1)*(1+x^ithprime(n)))) end:
a:= n-> max(coeffs(b(n))):
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MATHEMATICA
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Table[Max[CoefficientList[Product[(1 + x^Prime[k]), {k, 2, n}], x]], {n, 0, 40}]
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PROG
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(PARI) a(n) = vecmax(Vec(prod(i=2, n, 1+x^prime(i)))); \\ Michel Marcus, Jan 29 2024
(Python)
from collections import Counter
from sympy import prime
c = {0:1}
for i in range(2, n+1):
p, d = prime(i), Counter(c)
for k in c:
d[k+p] += c[k]
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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