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

1,1

Links

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

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 *)

Crossrefs

Cf. A000010, A003415, A166374, A190403.

Sequence in context: A169926 A140164 A160730 * A175300 A316699 A132425

Adjacent sequences: A190399 A190400 A190401 * A190403 A190404 A190405

Keyword

nonn

Author

Paolo P. Lava, May 10 2011

Status

approved