A230545 - OEIS

%I #27 Mar 22 2019 12:09:28

%S 8,12,100,140,243,405,1372,46875,56644,64827,98260,101871,107811,

%T 129375,230692,243675,300820,644204,851175,1953125,3828125,7948395,

%U 19307236,28218268,36517316,69330772,70174377,93961125,115008417,173353125,181010116,267603885,404021709

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

%C Subsequence of A002808. - _Altug Alkan_, Oct 07 2015

%H Giovanni Resta, <a href="/A230545/b230545.txt">Table of n, a(n) for n = 1..108</a> (terms < 10^13)

%e For n = 1372 we have phi(n) = 588, n' = 1960 and 1960 = 1372 + 588.

%p with(numtheory); P:= proc(q) local a1, a2, n, p;

%p for n from 1 to q do a1:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);

%p if a1=n+phi(n) then print(n); fi; od; end: P(10^6);

%o (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 Cf. A000010, A003415, A260624.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Oct 25 2013

%E a(21)-a(33) from _Giovanni Resta_, Oct 25 2013