A190402 Number n for which phi(n) = phi(n'), where phi is the Euler totient function and n' the arithmetic derivative of n.

2, 4, 8, 14, 20, 27, 45, 52, 75, 148, 195, 244, 292, 364, 628, 729, 772, 1108, 1196, 1215, 1252, 1406, 1552, 1588, 1684, 1701, 1828, 2164, 2452, 2644, 2692, 2924, 2932, 3028, 3125, 3508, 3825, 3982, 3988, 4372, 4462, 4612, 4804, 4852, 4948, 5284, 5524

Offset: 1

Author

Paolo P. Lava, May 10 2011

Keywords

• nonn

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A000010, A003415, A166374, A190403.

Programs

Maple

with(numtheory);
P:=proc(i)
local f,n,p,pfs;
for n from 1 to i do
    pfs:=ifactors(n)[2];
    f:=n*add(op(2,p)/op(1,p),p=pfs);
    if phi(n)=phi(f) then print(n); fi;
od;
end:
P(1000);

Mathematica

d[0] = d[1] = 0; d[n_] := n*Total[f = FactorInteger[n]; f[[All, 2]]/f[[All, 1]] ]; Reap[For[n = 1, n < 6000, n++, If[EulerPhi[n] == EulerPhi[d[n]], Sow[n]]]][[2, 1]] (* Jean-François Alcover, Apr 22 2015 *)