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

8, 12, 100, 140, 243, 405, 1372, 46875, 56644, 64827, 98260, 101871, 107811, 129375, 230692, 243675, 300820, 644204, 851175, 1953125, 3828125, 7948395, 19307236, 28218268, 36517316, 69330772, 70174377, 93961125, 115008417, 173353125, 181010116, 267603885, 404021709

Offset: 1

Author

Paolo P. Lava, Oct 25 2013

Keywords

• nonn

Comments

Subsequence of A002808. - Altug Alkan, Oct 07 2015

Examples

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..108 (terms < 10^13)

Crossrefs

Cf. A000010, A003415, A260624.

Programs

Maple

with(numtheory); P:= proc(q) local a1, a2, n, p;
for n from 1 to q do a1:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);
if a1=n+phi(n) then print(n); fi; od; end: P(10^6);

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

Extensions

a(21)-a(33) from Giovanni Resta, Oct 25 2013