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
Keywords
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