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A066087
a(n) = gcd(sigma(n), phi(n)) - gcd(sigma(rad(n)), phi(rad(n))); rad = A007947.
6
0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 1, -1, 0, -4, 0, 4, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -4, -2, 0, 0, 0, 0, -1, 0, 0, -4, 0, 0, 0, 18, 0, -2, 0, 2, 0, 0, 0, 2, 0, -3, 8, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 12, -6
OFFSET
1,12
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
A009223(n) - A066086(n) = gcd(sigma(n), phi(n)) - gcd(sigma(A007947(n)), phi(A007947(n))).
MATHEMATICA
Table[GCD[DivisorSigma[1, n], EulerPhi@ n] - GCD[DivisorSigma[1, #], EulerPhi@ #] &[Times @@ FactorInteger[n][[All, 1]]], {n, 120}] (* Michael De Vlieger, Feb 19 2017 *)
PROG
(PARI) rad(f)=for(i=1, #f~, f[i, 2]=1); f
g(f)=gcd(sigma(f), eulerphi(f))
a(n)=my(f=factor(n), k=rad(f)); g(f)-g(k) \\ Charles R Greathouse IV, Dec 09 2013
KEYWORD
sign
AUTHOR
Labos Elemer, Dec 04 2001
STATUS
approved