A076486 Solutions to gcd(sigma(x), phi(x)) < gcd(sigma(core(x)), phi(core(x))), i.e., when A009223(x) < A066086(x) or if A066087(x) < 0.
9, 25, 28, 36, 45, 50, 52, 75, 76, 81, 84, 90, 98, 100, 117, 121, 124, 144, 148, 150, 153, 156, 175, 180, 208, 225, 228, 234, 242, 244, 245, 252, 261, 268, 275, 289, 292, 300, 304, 306, 316, 324, 325, 333, 338, 360, 364, 369, 372, 380, 388, 392, 400, 405, 412
Offset: 1
Keywords
Examples
For n=9: sigma(9)=13, phi(9)=6, gcd(13,6)=1, core(9)=3, sigma(3)=4, phi(3)=2, gcd(4,2)=2.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] cor[x_] := Apply[Times, ba[x]] g1[x_] := GCD[DivisorSigma[1, x], EulerPhi[x]] g2[x_] := GCD[DivisorSigma[1, cor[x]], EulerPhi[cor[x]]] Do[s1=g1[n]; s2=g2[n]; If[Greater[s2, s1], Print[n]], {n, 1, 256}]