A076487 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.
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 77, 78, 79, 80, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95
Offset: 1
Keywords
Examples
For n=20: sigma(20)=42, phi(20)=8, gcd(42,8)=2, core(20)=10, sigma(10)=18, phi(10)=4, gcd(18,4)=2, so A009223(20) = A066086(20)=2.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Crossrefs
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[Equal[s2, s1], Print[n]], {n, 1, 256}] -
PARI
isok(n) = my(c=core(n)); gcd(sigma(n), eulerphi(n)) == gcd(sigma(c), eulerphi(c)); \\ Michel Marcus, Jul 30 2017
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