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A350514 Maximal coefficient of Product_{j=1..n} (1 - x^prime(j)).

%I A350514 #45 Jun 02 2022 08:59:23
%S A350514 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 A350514 1561,2701,4817,8514,15030,26490,47200,84622,151809,273912,496807,
%U A350514 900595,1643185,2999837,5498916,10111429,18596096,34306158,63585519,118215700
%N A350514 Maximal coefficient of Product_{j=1..n} (1 - x^prime(j)).
%H A350514 Alois P. Heinz, <a href="/A350514/b350514.txt">Table of n, a(n) for n = 0..500</a>
%p A350514 b:= proc(n) option remember; `if`(n=0, 1,
%p A350514       expand((1-x^ithprime(n))*b(n-1)))
%p A350514     end:
%p A350514 a:= n-> max(coeffs(b(n))):
%p A350514 seq(a(n), n=0..60);
%t A350514 a[n_] := Times@@(1-x^Prime[Range[n]])//Expand//CoefficientList[#, x]&//Max;
%t A350514 Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Jun 02 2022 *)
%o A350514 (Python)
%o A350514 from sympy.abc import x
%o A350514 from sympy import prime, prod
%o A350514 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 A350514 (PARI) a(n) = vecmax(Vec(prod(j=1, n, 1-'x^prime(j)))); \\ _Michel Marcus_, Jan 04 2022
%Y A350514 Cf. A000040, A007504, A046675, A086376, A350457.
%K A350514 nonn
%O A350514 0,11
%A A350514 _Alois P. Heinz_, Jan 02 2022