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A272529 Numbers n such that the arithmetic derivative of the cototient(n) is equal to the totient(n). 1
8, 189, 405, 465, 2187, 2565, 3483, 6885, 41283, 46875, 389691, 796875, 13410657, 837134375, 12557032155, 23202024507, 31335628125, 38655885285, 115964116965 (list; graph; refs; listen; history; text; internal format)
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: A197233 A163701 A244438 * A198282 A177147 A251669

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

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Last modified October 16 15:08 EDT 2021. Contains 348042 sequences. (Running on oeis4.)