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A340190
Möbius transform of A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).
4
1, 0, 1, 0, 3, -1, 5, 0, 0, -3, 9, 0, 11, -5, -1, 0, 15, 0, 17, 0, -3, -9, 21, 0, 0, -11, 0, 2, 27, 1, 29, 0, -7, -15, -5, 0, 35, -17, -9, 0, 39, 3, 41, 0, 4, -21, 45, 0, 0, 0, -13, 2, 51, 0, -9, -2, -15, -27, 57, 0, 59, -29, 0, 0, 1, 11, 65, 0, -19, 7, 69, 0, 71, -35, 0, 2, -11, 9, 77, 0, 0, -39, 81, -2, -3, -41, -25
OFFSET
1,5
FORMULA
a(n) = Sum_{d|n} A008683(n/d) * A063994(d).
a(n) = A063994(n) - A340191(n).
PROG
(PARI)
A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
A340190(n) = sumdiv(n, d, moebius(n/d)*A063994(d));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Dec 31 2020
STATUS
approved