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

0,11

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

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 *)

Prog

(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
(PARI) a(n) = vecmax(Vec(prod(j=1, n, 1-'x^prime(j)))); \\ Michel Marcus, Jan 04 2022

Crossrefs

Cf. A000040, A007504, A046675, A086376, A350457.

Sequence in context: A176975 A333374 A098523 * A308620 A339711 A048185

Adjacent sequences: A350511 A350512 A350513 * A350515 A350516 A350517

Keyword

nonn

Author

Alois P. Heinz, Jan 02 2022

Status

approved