A350457 - OEIS

%I #22 Feb 26 2022 04:56:56

%S 1,1,1,2,2,2,4,4,7,10,16,27,45,79,139,249,439,784,1419,2574,4703,8682,

%T 16021,29720,55146,102170,190274,356804,671224,1269022,2404289,

%U 4521836,8535117,16134474,30635869,58062404,110496946,210500898,401422210,767158570,1467402238

%N Maximal coefficient of (1 + x^2) * (1 + x^3) * (1 + x^5) * ... * (1 + x^prime(n)).

%H Alois P. Heinz, <a href="/A350457/b350457.txt">Table of n, a(n) for n = 0..700</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..40);  # _Alois P. Heinz_, Jan 01 2022

%t b[n_] := b[n] = If[n == 0, 1, Expand[(1 + x^Prime[n])*b[n - 1]]];

%t a[n_] := Max[CoefficientList[b[n], x]];

%t Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Feb 26 2022, after _Alois P. Heinz_ *)

%o (PARI) a(n) = vecmax(Vec(prod(k=1, n, 1 + x^prime(k)))); \\ _Michel Marcus_, Jan 01 2022

%o (Python)

%o from sympy.abc import x

%o from sympy import prime, prod

%o 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

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

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Jan 01 2022