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A248817 Numbers that are equal to the arithmetic derivative of their cototient. 1
12, 32, 44, 332, 5103, 10935, 12555, 59049, 69255, 94041, 185895, 1114641, 1265625, 1453125, 3639916, 8015625, 10475212, 10521657, 12254625, 21515625, 146484375, 155649627, 178598385, 244603436, 362087739, 1408107267, 1540368225, 2186172700, 2490234375 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Solutions of the equation n = (n - phi(n))’.

a(32) > 10^11. - Hiroaki Yamanouchi, Sep 11 2015

LINKS

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..31

EXAMPLE

Cototient of 12 is 12 - phi(12) = 12 - 4 = 8 and the arithmetic derivative of 8 is 12.

MAPLE

with(numtheory); P:= proc(q) local a, n, p; for n from 1 to q do

a:=(n-phi(n))*add(op(2, p)/op(1, p), p=ifactors(n-phi(n))[2]);

if n=a then print(n); fi; od; end: P(10^6);

CROSSREFS

Cf. A003415, A051953.

Sequence in context: A242371 A118785 A071336 * A051519 A305074 A166959

Adjacent sequences:  A248814 A248815 A248816 * A248818 A248819 A248820

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Oct 15 2014

EXTENSIONS

a(21)-a(29) from Hiroaki Yamanouchi, Sep 11 2015

STATUS

approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)