login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n) is the constant term in the expansion of Product_{d|n} (x^d + 1 + 1/x^d).
2

%I #12 Feb 05 2024 21:00:44

%S 1,1,1,1,1,5,1,1,1,1,1,23,1,1,1,1,1,13,1,13,1,1,1,103,1,1,1,7,1,77,1,

%T 1,1,1,1,175,1,1,1,63,1,49,1,1,5,1,1,463,1,1,1,1,1,41,1,39,1,1,1,2975,

%U 1,1,3,1,1,33,1,1,1,25,1,2363,1,1,1,1,1,25,1,261

%N a(n) is the constant term in the expansion of Product_{d|n} (x^d + 1 + 1/x^d).

%C a(n) is the number of solutions to 0 = Sum_{d|n} c_i * d with c_i in {-1,0,1}, i=1..tau(n), tau = A000005.

%H Alois P. Heinz, <a href="/A369874/b369874.txt">Table of n, a(n) for n = 1..20000</a>

%t Table[Coefficient[Product[(x^d + 1 + 1/x^d), {d, Divisors[n]}], x, 0], {n, 1, 80}]

%o (Python)

%o from collections import Counter

%o from sympy import divisors

%o def A369874(n):

%o c = {0:1}

%o for d in divisors(n,generator=True):

%o b = Counter(c)

%o for j in c:

%o a = c[j]

%o b[j+d] += a

%o b[j-d] += a

%o c = b

%o return c[0] # _Chai Wah Wu_, Feb 05 2024

%Y Cf. A000005, A007576, A033630, A083206, A369873.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Feb 03 2024