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A272528 Numbers n such that the arithmetic derivative of the totient(n) is equal to the cototient(n). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
Sequence in context: A060305 A009141 A090069 * A195676 A027299 A321067
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, May 02 2016
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)