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A329643
a(n) = Sum_{d|n} [-1 == A008683(n/d)] * A323244(d), where A323244(x) gives the deficiency of A156552(x).
4
0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 6, 0, 2, 2, 6, 0, 4, 0, 7, 2, 2, 0, 16, 1, 2, 0, 18, 0, 11, 0, 6, 2, 2, 2, 22, 0, 2, 2, 24, 0, 17, 0, 20, 2, 2, 0, 28, 1, 1, 2, 48, 0, 16, 2, 28, 2, 2, 0, 39, 0, 2, -3, 30, 2, 36, 0, 84, 2, 19, 0, 36, 0, 2, -2, 258, 2, 38, 0, 28, 4, 2, 0, 69, 2, 2, 2, 72, 0, 31, 2, 228, 2, 2, 2, 76, 0, 4, 14, 37, 0, 94, 0, 136, -3
OFFSET
1,6
FORMULA
a(n) = Sum_{d|n} [-1 == A008683(n/d)] * (2*A156552(d) - A323243(d)).
a(n) = A329642(n) - A329644(n).
For all n, a(A000040(n)) = 0, a(A006881(n)) = 2.
PROG
(PARI)
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
A323243(n) = if(1==n, 0, sigma(A156552(n)));
A329643(n) = sumdiv(n, d, (-1==moebius(n/d))*((2*A156552(d))-A323243(d)));
CROSSREFS
Cf. A329646 (inverse Möbius transform).
Sequence in context: A071459 A319164 A070288 * A352697 A165414 A330868
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 21 2019
STATUS
approved