A226384 -id:A226384 - cp's OEIS frontend

A226386 Numbers n such that rad(phi(n)) < phi(rad(n)), where rad(n) is the squarefree kernel of n, and phi is Euler's totient function.

5, 10, 13, 15, 17, 19, 20, 21, 26, 29, 30, 33, 34, 35, 37, 38, 39, 40, 41, 42, 45, 51, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 70, 73, 74, 76, 77, 78, 80, 82, 84, 85, 87, 89, 90, 91, 93, 95, 97, 101, 102, 104, 105, 106, 109, 110, 111, 113, 114, 115

Offset: 1

José María Grau Ribas, Jun 05 2013

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A007947, A000010, A226384.

rad[n_] := Product[fa[n][[i, 1]], {i, Length[fa[n]]}]; fa = FactorInteger; Select[Range[500], rad[EulerPhi[#]] < EulerPhi[rad[#]] &]

rad(n)=my(f=factor(n)[,1]);prod(i=1,#f,f[i])
is(n)=my(f=factor(n)[,1],r=prod(i=1,#f,f[i]),ph=prod(i=1,#f,f[i]-1)*n/r); rad(ph)Charles R Greathouse IV, Dec 13 2013

A226385 Numbers n such that rad(phi(n)) > phi(rad(n)), where rad(n) is the squarefree kernel of n, and phi is Euler's totient function.

Original entry on oeis.org

4, 8, 9, 16, 18, 25, 27, 32, 36, 49, 50, 54, 64, 72, 75, 81, 98, 99, 100, 108, 121, 125, 128, 144, 147, 150, 162, 169, 175, 196, 198, 200, 207, 216, 225, 242, 243, 245, 250, 256, 288, 289, 294, 297, 300, 324, 338, 343, 350, 361, 363, 375, 392, 396, 400, 414

Offset: 1

José María Grau Ribas, Jun 05 2013

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A007947, A000010, A226384, A226386.

rad[n_] := Product[fa[n][[i, 1]], {i,Length[fa[n]]}]; fa = FactorInteger; Select[Range[500], rad[EulerPhi[#]] > EulerPhi[rad[#]] &]

rad(n)=my(f=factor(n)[,1]); prod(i=1,#f,f[i])
is(n)=rad(eulerphi(n))>eulerphi(rad(n)) \\ Charles R Greathouse IV, Dec 27 2013

cp's OEIS Frontend

A226386 Numbers n such that rad(phi(n)) < phi(rad(n)), where rad(n) is the squarefree kernel of n, and phi is Euler's totient function.

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