A260962 Numbers k such that phi(k) = phi'(k'), where phi(k) is the Euler totient function of k and k' is the arithmetic derivative of k.

8, 26, 122, 351, 31195, 47201, 51243, 118265, 300985, 472491, 672147, 673863, 850969, 931383, 1440625, 3000927, 3669213, 3740755, 4688645, 4822143, 4864175, 11224565, 13897079, 13949343, 16362857, 16744355, 18844265, 19536205, 35580099, 38656975, 42056215, 46294105

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

Example

Arithmetic derivative of 26 is 15, phi(15) = 8 and 8' = 12 that is equal to phi(26).

Maple

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

Mathematica

f[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger@ Abs@ n]]; Select[Range@ 100000, f@ EulerPhi@ f@ # == EulerPhi@ # &] (* Michael De Vlieger, Aug 07 2015, after Michael Somos at A003415 *)

Crossrefs

Cf. A000010, A003415, A190402, A260961.

Sequence in context: A082573 A112645 A220713 * A274733 A223312 A194997

Adjacent sequences: A260959 A260960 A260961 * A260963 A260964 A260965

Keyword

nonn,easy

Author

Paolo P. Lava, Aug 06 2015

Status

approved