OFFSET
1,1
COMMENTS
Solutions of the equation n = (phi(n))’.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..500 from Paolo P. Lava)
EXAMPLE
Euler totient function of 32 is 16 and the arithmetic derivative of 16 is 32.
MAPLE
with(numtheory): P:= proc(q) local a, n, p; for n from 1 to q do
a:=phi(n)*add(op(2, p)/op(1, p), p=ifactors(phi(n))[2]);
if n=a then print(n); fi; od; end: P(10^9);
MATHEMATICA
deriv[n_] := n*Total[#2/#1 & @@@ FactorInteger[n]]; aQ[1] = 1; aQ[n_] := deriv[EulerPhi[n]] == n; Select[Range[25000], aQ] (* Amiram Eldar, Jul 11 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Oct 15 2014
STATUS
approved