login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A350514
Maximal coefficient of Product_{j=1..n} (1 - x^prime(j)).
3
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 02 2022
STATUS
approved