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A347231
Difference between A344695 [gcd(psi(n),sigma(n))] and its Möbius transform.
3
0, 1, 1, 3, 1, 6, 1, 1, 4, 8, 1, 10, 1, 10, 9, 3, 1, 9, 1, 16, 11, 14, 1, 6, 6, 16, 1, 22, 1, 42, 1, 1, 15, 20, 13, -5, 1, 22, 17, 8, 1, 54, 1, 34, 21, 26, 1, 10, 8, 13, 21, 40, 1, 6, 17, 10, 23, 32, 1, 54, 1, 34, 29, 3, 19, 78, 1, 52, 27, 74, 1, 9, 1, 40, 19, 58, 19, 90, 1, 16, 4, 44, 1, 74, 23, 46, 33, 14, 1, 48
OFFSET
1,4
LINKS
FORMULA
a(n) = A344695(n) - A347230(n).
a(n) = -Sum_{d|n, d<n} A008683(n/d) * A344695(d).
PROG
(PARI)
A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A344695(n) = gcd(sigma(n), A001615(n));
A347231(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A344695(d));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Aug 25 2021
STATUS
approved