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

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..700

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 *)

Prog

(PARI) a(n) = vecmax(Vec(prod(k=1, n, 1 + x^prime(k)))); \\ Michel Marcus, Jan 01 2022
(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

Crossrefs

Cf. A000040, A000586, A007504, A025591, A160235.

Sequence in context: A326545 A326684 A366598 * A010238 A178799 A360360

Adjacent sequences: A350454 A350455 A350456 * A350458 A350459 A350460

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 01 2022

Status

approved