A369788 Number of different coefficient values in expansion of Product_{k=1..n} (1+x^prime(k)).

1, 2, 2, 3, 3, 3, 5, 5, 8, 11, 17, 27, 38, 66, 85, 121, 152, 185, 216, 249, 285, 325, 363, 406, 449, 499, 549, 601, 654, 709, 765, 829, 894, 963, 1032, 1107, 1182, 1261, 1342, 1426, 1512, 1602, 1692, 1788, 1884, 1983, 2082, 2188, 2299, 2413, 2527, 2644, 2763, 2884, 3009

Offset: 0

Author

Seiichi Manyama, Feb 01 2024

Keywords

• nonn

Crossrefs

Cf. A000040, A000586, A007504, A369789.

Programs

PARI

a(n) = #Set(Vec(prod(k=1, n, 1+x^prime(k))));

Python

from collections import Counter
from sympy import prime
def A369788(n):
    c = {0:1}
    for k in range(1,n+1):
        m, d = prime(k), Counter(c)
        for j in c:
            d[j+m] += c[j]
        c = d
    return len(set(c.values()))+int(max(c)+1>len(c)) # Chai Wah Wu, Feb 01 2024