A369775 - OEIS

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)).

1, 1, 2, 5, 16, 65, 293, 1807, 12946, 106475, 972260, 9858553, 109451903, 1323071345, 17398667717, 247055196932, 3753507625272, 60680317203979, 1043036844360792, 18969267205680868, 364107881070036688, 7366172106829696356, 156467911373737550264

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

MATHEMATICA

Table[Max[CoefficientList[Product[(1 + Sum[x^Prime[j], {j, 1, i}]), {i, 1, n}], x]], {n, 0, 22}]

PROG

(PARI) a(n) = vecmax(Vec(prod(k=1, n, 1 + sum(i=1, k, x^prime(i))))); \\ Michel Marcus, Feb 01 2024

(Python)

from collections import Counter

from sympy import prime, primerange

def A369775(n):

if n == 0: return 1

c, p = {0:1}, list(primerange(prime(n)+1))

for k in range(1, n+1):

d = Counter(c)

for j in c:

a = c[j]

for i in p[:k]:

d[j+i] += a

c = d

return max(c.values()) # Chai Wah Wu, Feb 01 2024

CROSSREFS

Cf. A000040, A000140, A039831, A350457, A359328.

Sequence in context: A131178 A003149 A027046 * A268170 A000522 A182290

Adjacent sequences: A369772 A369773 A369774 * A369776 A369777 A369778

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 31 2024

STATUS

approved