A319999 -id:A319999 - cp's OEIS frontend

A319993 a(n) = A319997(n) / A173557(n).

1, -1, 1, 0, 1, -1, 1, 0, 3, -1, 1, 0, 1, -1, 1, 0, 1, -3, 1, 0, 1, -1, 1, 0, 5, -1, 9, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 3, -1, 1, 0, 7, -5, 1, 0, 1, -9, 1, 0, 1, -1, 1, 0, 1, -1, 3, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 5, 0, 1, -1, 1, 0, 27, -1, 1, 0, 1, -1, 1, 0, 1, -3, 1, 0, 1, -1, 1, 0, 1, -7, 3, 0, 1, -1, 1, 0, 1

Offset: 1

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Antti Karttunen, Nov 08 2018

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Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A003557, A173557, A319997, A319999.

A319993(n) =  { my(f=factor(n)); prod(i=1,#f~,if(2==f[i,1],-(1==f[i,2]),(f[i,1]^(f[i,2]-1)))); };

A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
A319997(n) = sumdiv(n,d,(d%2)*moebius(n/d)*d);
A319993(n) = (A319997(n)/A173557(n));

Multiplicative with a(2^1) = -1, a(2^e) = 0 for e > 1, and a(p^e) = p^(e-1) when p is an odd prime.
a(n) = A319997(n) / A173557(n).
a(2n) = A003557(2n) - 2*A003557(n), a(2n+1) = A003557(2n+1).

cp's OEIS Frontend

A319993 a(n) = A319997(n) / A173557(n).

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