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

1,1

Comments

Subsequence of A002808. - Altug Alkan, Oct 07 2015

Links

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

Example

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

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);

Prog

(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

Crossrefs

Cf. A000010, A003415, A260624.

Sequence in context: A162466 A098664 A266800 * A180922 A083128 A196077

Adjacent sequences: A230542 A230543 A230544 * A230546 A230547 A230548

Keyword

nonn

Author

Paolo P. Lava, Oct 25 2013

Extensions

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

Status

approved