login
A190402
Number n for which phi(n) = phi(n'), where phi is the Euler totient function and n' the arithmetic derivative of n.
8
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
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
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 10 2011
STATUS
approved