A272529 Numbers n such that the arithmetic derivative of the cototient(n) is equal to the totient(n).

8, 189, 405, 465, 2187, 2565, 3483, 6885, 41283, 46875, 389691, 796875, 13410657, 837134375, 12557032155, 23202024507, 31335628125, 38655885285, 115964116965

Offset

1,1

Comments

a(15) > 10^10. - Amiram Eldar, Jan 30 2019

1.25*10^11 < a(20) <= 13421772796875. - Giovanni Resta, Apr 15 2019

Links

Table of n, a(n) for n=1..19.

Example

(8 - phi(8))’ = (8 - 4)’ = 4’ = 4 = phi(8) ;
(189 - phi(189))’ = (189 - 108)’ = 81’ = 108 = phi(189).

Maple

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

Mathematica

Select[Range[10^6], 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, A272528.

Sequence in context: A163701 A354407 A244438 * A198282 A177147 A366150

Adjacent sequences: A272526 A272527 A272528 * A272530 A272531 A272532

Keyword

nonn,more

Author

Paolo P. Lava, May 02 2016

Extensions

a(14) from Amiram Eldar, Jan 30 2019

a(15)-a(19) from Giovanni Resta, Apr 15 2019

Status

approved