A077103 Numbers n such that gcd(a,b) is not equal to gcd(a+b,a-b), where a=sigma(n)=A000203(n) and b=phi(n)=A000010(n).

1, 2, 12, 15, 30, 39, 44, 55, 56, 76, 78, 87, 95, 99, 110, 111, 125, 140, 143, 147, 159, 171, 172, 174, 175, 183, 184, 190, 198, 215, 216, 222, 236, 247, 250, 252, 264, 268, 286, 287, 294, 295, 303, 315, 318, 319, 327, 332, 335, 336, 342, 350, 357, 363, 364

Offset: 1

Author

Labos Elemer, Nov 12 2002

Keywords

• nonn

Examples

			n=76: a=sigma(76)=140, b=phi(76)=36, a+b=176, a-b=104, gcd(a,b) = gcd(140,36) = 4 < gcd(a+b,a-b) = gcd(176,104) = 8.
		

Crossrefs

Cf. A000010, A000203, A051612, A065387, A055008, A077099.

Programs

Mathematica

Do[s=GCD[a=DivisorSigma[1, n], b=EulerPhi[n]]; s1=GCD[a+b, a-b]; If[ !Equal[s, s1], Print[{n, a, b, a+b, a-b, s, s1, s1/s}]], {n, 1, 1000}]

Formula

gcd(A000010(n), A000203(n)) is not equal to gcd(A065387(n), A051612(n)); or A055008(n) is not equal to A077099(n).