A350457 Maximal coefficient of (1 + x^2) * (1 + x^3) * (1 + x^5) * ... * (1 + x^prime(n)).
1, 1, 1, 2, 2, 2, 4, 4, 7, 10, 16, 27, 45, 79, 139, 249, 439, 784, 1419, 2574, 4703, 8682, 16021, 29720, 55146, 102170, 190274, 356804, 671224, 1269022, 2404289, 4521836, 8535117, 16134474, 30635869, 58062404, 110496946, 210500898, 401422210, 767158570, 1467402238
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..700
Programs
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Maple
b:= proc(n) option remember; `if`(n=0, 1, expand((1+x^ithprime(n))*b(n-1))) end: a:= n-> max(coeffs(b(n))): seq(a(n), n=0..40); # Alois P. Heinz, Jan 01 2022 -
Mathematica
b[n_] := b[n] = If[n == 0, 1, Expand[(1 + x^Prime[n])*b[n - 1]]]; a[n_] := Max[CoefficientList[b[n], x]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 26 2022, after Alois P. Heinz *) -
PARI
a(n) = vecmax(Vec(prod(k=1, n, 1 + x^prime(k)))); \\ Michel Marcus, Jan 01 2022
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Python
from sympy.abc import x from sympy import prime, prod def A350457(n): return 1 if n == 0 else max(prod(1+x**prime(i) for i in range(1,n+1)).as_poly().coeffs()) # Chai Wah Wu, Jan 03 2022