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A369873 a(n) is the constant term in the expansion of Product_{d|n} (x^d + 1/x^d).

%I A369873 #25 Jan 20 2025 10:52:24
%S A369873 0,0,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,0,0,2,0,0,0,6,0,0,0,2,0,6,0,0,0,0,
%T A369873 0,0,0,0,0,4,0,4,0,0,0,0,0,10,0,0,0,0,0,4,0,2,0,0,0,34,0,0,0,0,0,4,0,
%U A369873 0,0,2,0,0,0,0,0,0,0,4,0,6,0,0,0,28,0,0,0,2,0,26,0,0,0,0,0,22,0,0,0,0,0,4,0,2,0
%N A369873 a(n) is the constant term in the expansion of Product_{d|n} (x^d + 1/x^d).
%C A369873 a(n) is the number of solutions to 0 = Sum_{d|n} c_i * d with c_i in {-1,1}, i=1..tau(n), tau = A000005.
%H A369873 Antti Karttunen, <a href="/A369873/b369873.txt">Table of n, a(n) for n = 1..10000</a>
%F A369873 From _Joerg Arndt_, Feb 04 2024: (Start)
%F A369873 a(n) != 0 (only) for n in A083207.
%F A369873 a(n) = 2 * A083206(n). (End)
%t A369873 Table[Coefficient[Product[(x^d + 1/x^d), {d, Divisors[n]}], x, 0], {n, 1, 90}]
%o A369873 (Python)
%o A369873 from collections import Counter
%o A369873 from sympy import divisors
%o A369873 def A369873(n):
%o A369873     c = {0:1}
%o A369873     for d in divisors(n,generator=True):
%o A369873         b = Counter()
%o A369873         for j in c:
%o A369873             a = c[j]
%o A369873             b[j+d] += a
%o A369873             b[j-d] += a
%o A369873         c = b
%o A369873     return c[0] # _Chai Wah Wu_, Feb 05 2024
%o A369873 (PARI) A369873(n) = { my(s=sigma(n),p=1); if(s%2 || s < 2*n, 0, fordiv(n, d, p *= ('x^d + 'x^-d)); polcoeff(p, 0)); }; \\ (cf. also code in A083206 and A379504) - _Antti Karttunen_, Jan 20 2025
%Y A369873 Cf. A000005, A033630, A063865, A083206, A083207, A379504.
%K A369873 nonn
%O A369873 1,6
%A A369873 _Ilya Gutkovskiy_, Feb 03 2024
%E A369873 Data section extended to a(105) by _Antti Karttunen_, Jan 20 2025