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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.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Aug 06 2015
STATUS
approved