A350514 Maximal coefficient of Product_{j=1..n} (1 - x^prime(j)).
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 6, 8, 12, 17, 30, 41, 70, 107, 186, 307, 531, 887, 1561, 2701, 4817, 8514, 15030, 26490, 47200, 84622, 151809, 273912, 496807, 900595, 1643185, 2999837, 5498916, 10111429, 18596096, 34306158, 63585519, 118215700
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..500
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..60); -
Mathematica
a[n_] := Times@@(1-x^Prime[Range[n]])//Expand//CoefficientList[#, x]&//Max; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Jun 02 2022 *) -
PARI
a(n) = vecmax(Vec(prod(j=1, n, 1-'x^prime(j)))); \\ Michel Marcus, Jan 04 2022
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Python
from sympy.abc import x from sympy import prime, prod def A350514(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 04 2022