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

Author

Paolo P. Lava, Aug 06 2015

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

Cf. A000010, A003415, A190402, A260961.

Programs

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 *)