A272528 Numbers n such that the arithmetic derivative of the totient(n) is equal to the cototient(n).

1, 3, 8, 20, 28, 44, 48, 92, 188, 228, 236, 324, 332, 428, 668, 716, 756, 908, 1052, 1388, 1436, 1532, 1868, 1916, 2012, 2252, 2348, 2876, 3356, 3452, 3548, 3932, 4076, 4748, 5132, 5228, 5276, 5468, 5756, 5948, 6092, 6476, 7292, 7628, 8108, 8156, 8252, 8396, 8828

Offset

1,2

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

phi(92)' = 44' = 48 = 92 - phi(92);
phi(332)' = 164' = 168 = 332 - phi(332).

Maple

with(numtheory): P:= proc(q) local n, p; for n from 1 to q do
if phi(n)*add(op(2, p)/op(1, p), p=ifactors(phi(n))[2])=n-phi(n) then print(n);
fi; od; end: P(10^9);

Mathematica

Select[Range[10^4], Function[m, Function[k, If[Abs@k < 2, 0, k Total[#2/#1 & @@@ FactorInteger[Abs@ k]]]]@ m == # - m]@ EulerPhi@ # &] (* Michael De Vlieger, May 02 2016, after Michael Somos at A003415 *)

Crossrefs

Cf. A000010, A003415, A051953, A272529.

Sequence in context: A060305 A009141 A090069 * A195676 A027299 A321067

Adjacent sequences: A272525 A272526 A272527 * A272529 A272530 A272531

Keyword

nonn,easy

Author

Paolo P. Lava, May 02 2016

Status

approved