A066087 - OEIS

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A066087

a(n) = gcd(sigma(n), phi(n)) - gcd(sigma(rad(n)), phi(rad(n))); rad = A007947.

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

(list; graph; refs; listen; history; text; internal format)

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

CROSSREFS

Cf. A048250, A023900, A000203, A007947, A000010, A009223, A066086.

Sequence in context: A060862 A325801 A325194 * A294927 A080224 A341508

Adjacent sequences: A066084 A066085 A066086 * A066088 A066089 A066090

KEYWORD

sign

AUTHOR

Labos Elemer, Dec 04 2001

STATUS

approved