A369789 Number of different coefficient values in expansion of Product_{k=1..n} (1+x^prime(k))^2.

1, 3, 4, 5, 10, 20, 29, 47, 69, 92, 122, 153, 190, 231, 274, 321, 374, 433, 494, 561, 632, 705, 784, 867, 956, 1053, 1154, 1257, 1364, 1473, 1586, 1713, 1844, 1981, 2120, 2269, 2420, 2577, 2740, 2907, 3080, 3259, 3440, 3631, 3824, 4021, 4220, 4431, 4654, 4881, 5110

Offset: 0

Author

Seiichi Manyama, Feb 01 2024

Keywords

• nonn

Crossrefs

Cf. A280245, A369788.

Programs

PARI

a(n) = #Set(Vec(prod(k=1, n, (1+x^prime(k))^2)));

Python

from collections import Counter
from sympy import prime
def A369789(n):
    c = {0:1}
    for k in range(1,n+1):
        m, d = prime(k), Counter(c)
        for j in c:
            a = c[j]
            d[j+m] += a<<1
            d[j+(m<<1)] += a
        c = d
    return len(set(c.values()))+int(max(c)+1>len(c)) # Chai Wah Wu, Feb 01 2024