%I #45 Jun 02 2022 08:59:23

%S 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,

%T 1561,2701,4817,8514,15030,26490,47200,84622,151809,273912,496807,

%U 900595,1643185,2999837,5498916,10111429,18596096,34306158,63585519,118215700

%N Maximal coefficient of Product_{j=1..n} (1 - x^prime(j)).

%H Alois P. Heinz, <a href="/A350514/b350514.txt">Table of n, a(n) for n = 0..500</a>

%p b:= proc(n) option remember; `if`(n=0, 1,

%p expand((1-x^ithprime(n))*b(n-1)))

%p end:

%p a:= n-> max(coeffs(b(n))):

%p seq(a(n), n=0..60);

%t a[n_] := Times@@(1-x^Prime[Range[n]])//Expand//CoefficientList[#, x]&//Max;

%t Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Jun 02 2022 *)

%o (Python)

%o from sympy.abc import x

%o from sympy import prime, prod

%o 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

%o (PARI) a(n) = vecmax(Vec(prod(j=1, n, 1-'x^prime(j)))); \\ _Michel Marcus_, Jan 04 2022

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

%K nonn

%O 0,11

%A _Alois P. Heinz_, Jan 02 2022