cp's OEIS Frontend

A230545 Solutions of the equation n' = n + phi(n), where n' is the arithmetic derivative of n.

%I A230545 #27 Mar 22 2019 12:09:28
%S A230545 8,12,100,140,243,405,1372,46875,56644,64827,98260,101871,107811,
%T A230545 129375,230692,243675,300820,644204,851175,1953125,3828125,7948395,
%U A230545 19307236,28218268,36517316,69330772,70174377,93961125,115008417,173353125,181010116,267603885,404021709
%N A230545 Solutions of the equation n' = n + phi(n), where n' is the arithmetic derivative of n.
%C A230545 Subsequence of A002808. - _Altug Alkan_, Oct 07 2015
%H A230545 Giovanni Resta, <a href="/A230545/b230545.txt">Table of n, a(n) for n = 1..108</a> (terms < 10^13)
%e A230545 For n = 1372 we have phi(n) = 588, n' = 1960 and 1960 = 1372 + 588.
%p A230545 with(numtheory); P:= proc(q) local a1, a2, n, p;
%p A230545 for n from 1 to q do a1:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);
%p A230545 if a1=n+phi(n) then print(n); fi; od; end: P(10^6);
%o A230545 (PARI) for(n=2, 10^10, if((k = n + eulerphi(n)) && (d(n) = local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))) && k==d(n), print1(n", "))) \\ _Altug Alkan_, Oct 06 2015
%Y A230545 Cf. A000010, A003415, A260624.
%K A230545 nonn
%O A230545 1,1
%A A230545 _Paolo P. Lava_, Oct 25 2013
%E A230545 a(21)-a(33) from _Giovanni Resta_, Oct 25 2013