This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A329644 #35 Nov 23 2019 13:45:46
%S A329644 0,1,1,1,1,2,1,4,-1,3,1,5,1,14,0,0,1,9,1,12,-5,16,1,8,-5,44,4,5,1,2,1,
%T A329644 24,12,80,-4,-4,1,254,-14,0,1,22,1,47,7,224,1,24,-13,19,6,83,1,12,-21,
%U A329644 44,-14,746,1,14,1,1360,20,-8,8,9,1,131,252,24,1,12,1,3836,13,149,-12,71,1,56,-16,5456,1,-21,-74,12248,-350,-40,1
%N A329644 Möbius transform of A323244, the deficiency of A156552(n).
%C A329644 The first eleven zeros occur at n = 1, 15, 16, 40, 96, 119, 120, 160, 893, 2464, 6731. There are 3091 negative terms among the first 10000 terms.
%C A329644 Applying this function to the divisors of the first four terms of A324201 reveals the following pattern:
%C A329644 ------------------------------------------------------------------------------------
%C A329644 A324201(n) divisors a(n) applied Sum of positive
%C A329644 to each: terms, A329610
%C A329644 9: [1, 3, 9] -> [0, 1, -1] 1
%C A329644 125: [1, 5, 25, 125] -> [0, 1, -5, 4] 5
%C A329644 161051: [1, 11, 121, 1331, 14641, 161051] -> [0, 1, -29, 4, -240, 264] 269
%C A329644 410338673: [1, 17, 289, 4913, 83521, 1419857, 24137569, 410338673]
%C A329644 -> [0, 1, -125, 4, -1008, 1032, -5048, 5144] 6181
%C A329644 The positive and negative terms seem to alternate, and the fourth term (from case n=125 onward) is always 4. See also array A329637.
%H A329644 Antti Karttunen, <a href="/A329644/b329644.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%H A329644 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A329644 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A329644 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A329644 a(n) = Sum_{d|n} A008683(n/d) * A323244(d).
%F A329644 a(n) = Sum_{d|n} A008683(n/d) * (2*A156552(d) - A323243(d)).
%F A329644 a(1) = 0; for n > 1, a(n) = 2*A297112(n) - A324543(n) = 2^A297113(n) - A324543(n).
%F A329644 a(n) = A329642(n) - A329643(n).
%F A329644 For all n >= 1, a(A000040(n)^2) = A323244(A000040(n)^2)-1 = -A036563(n).
%F A329644 For all primes p, a(p^3) = A323244(p^3) - A323244(p^2) = 4.
%o A329644 (PARI)
%o A329644 A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A329644 A323244(n) = if(1==n, 0, my(k=A156552(n)); (2*k)-sigma(k));
%o A329644 A329644(n) = sumdiv(n,d,moebius(n/d)*A323244(d));
%Y A329644 Cf. A000203, A008683, A036563, A156552, A297112, A297113, A323243, A323244, A324543, A329610, A329637, A329638, A329639, A329645, A329646.
%K A329644 sign
%O A329644 1,6
%A A329644 _Antti Karttunen_, Nov 21 2019