A369789 - OEIS

%I #12 Feb 01 2024 16:50:33

%S 1,3,4,5,10,20,29,47,69,92,122,153,190,231,274,321,374,433,494,561,

%T 632,705,784,867,956,1053,1154,1257,1364,1473,1586,1713,1844,1981,

%U 2120,2269,2420,2577,2740,2907,3080,3259,3440,3631,3824,4021,4220,4431,4654,4881,5110

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

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

%o (Python)

%o from collections import Counter

%o from sympy import prime

%o def A369789(n):

%o     c = {0:1}

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

%o         m, d = prime(k), Counter(c)

%o         for j in c:

%o             a = c[j]

%o             d[j+m] += a<<1

%o             d[j+(m<<1)] += a

%o         c = d

%o     return len(set(c.values()))+int(max(c)+1>len(c)) # _Chai Wah Wu_, Feb 01 2024

%Y Cf. A280245, A369788.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 01 2024