A367843 Maximum of the absolute value of the coefficients of (1 - x^2) * (1 - x^3) * (1 - x^5) * ... * (1 - x^prime(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 6, 8, 12, 18, 30, 46, 70, 113, 186, 314, 531, 894, 1561, 2705, 4817, 8514, 15030, 26502, 47200, 84698, 151809, 273961, 496807, 900596, 1643185, 2999837, 5498916, 10111429, 18596096, 34306158, 63585519, 118215700

Offset: 0

Author

Ilya Gutkovskiy, Feb 06 2024

Keywords

• nonn

Crossrefs

Cf. A046675, A160089, A350457, A350514.

Programs

Mathematica

Table[Max[Abs[CoefficientList[Product[(1 - x^Prime[k]), {k, 1, n}], x]]], {n, 0, 46}]

Python

from collections import Counter
from sympy import prime
def A367843(n):
    c = {0:1}
    for k in range(1,n+1):
        p, b = prime(k), Counter(c)
        for j in c:
            b[j+p] -= c[j]
        c = b
    return max(map(abs,c.values())) # Chai Wah Wu, Feb 06 2024