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A369775 Maximal coefficient of (1 + x^2) * (1 + x^2 + x^3) * (1 + x^2 + x^3 + x^5) * ... * (1 + x^2 + ... + x^prime(n)).

%I A369775 #13 Feb 01 2024 16:24:21
%S A369775 1,1,2,5,16,65,293,1807,12946,106475,972260,9858553,109451903,
%T A369775 1323071345,17398667717,247055196932,3753507625272,60680317203979,
%U A369775 1043036844360792,18969267205680868,364107881070036688,7366172106829696356,156467911373737550264
%N A369775 Maximal coefficient of (1 + x^2) * (1 + x^2 + x^3) * (1 + x^2 + x^3 + x^5) * ... * (1 + x^2 + ... + x^prime(n)).
%t A369775 Table[Max[CoefficientList[Product[(1 + Sum[x^Prime[j], {j, 1, i}]), {i, 1, n}], x]], {n, 0, 22}]
%o A369775 (PARI) a(n) = vecmax(Vec(prod(k=1, n, 1 + sum(i=1, k, x^prime(i))))); \\ _Michel Marcus_, Feb 01 2024
%o A369775 (Python)
%o A369775 from collections import Counter
%o A369775 from sympy import prime, primerange
%o A369775 def A369775(n):
%o A369775     if n == 0: return 1
%o A369775     c, p = {0:1}, list(primerange(prime(n)+1))
%o A369775     for k in range(1,n+1):
%o A369775         d = Counter(c)
%o A369775         for j in c:
%o A369775             a = c[j]
%o A369775             for i in p[:k]:
%o A369775                 d[j+i] += a
%o A369775         c = d
%o A369775     return max(c.values()) # _Chai Wah Wu_, Feb 01 2024
%Y A369775 Cf. A000040, A000140, A039831, A350457, A359328.
%K A369775 nonn
%O A369775 0,3
%A A369775 _Ilya Gutkovskiy_, Jan 31 2024