A261432 Numbers n such that sigma(n) = phi'(n), where sigma(n) is the sum of the divisors of n and phi'(n) is the arithmetic derivative of the Euler totient function of n.

555, 2691, 9465, 10017, 16065, 42693, 64498, 108717, 164578, 194990, 204981, 222794, 488229, 1696130, 1705366, 1824506, 1838074, 1981588, 2079945, 2125112, 3823810, 4112090, 4292092, 4956105, 5354846, 5848766, 7462520, 7597834, 8394856

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Example

phi(555) = 288 and 288' = 912 = sigma(555);
phi(2691) = 1584 and 1584' = 4368 = sigma(2691).

Maple

with(numtheory): P:=proc(q) local a, n, p; for n from 1 to q do
a:=phi(n)*add(op(2, p)/op(1, p), p=ifactors(phi(n))[2]);
if a=sigma(n) then print(n); fi; od; end: P(10^9);

Mathematica

d[1]=0; d[n_] := Total[n / Divide@@@ FactorInteger@ n]; Select[Range[10^5], DivisorSigma[1, #] == d@ EulerPhi@ # &] (* Giovanni Resta, Aug 21 2015 *)

Crossrefs

Cf. A000010, A000203, A003415.

Sequence in context: A204365 A283158 A043511 * A104809 A233728 A233355

Adjacent sequences: A261429 A261430 A261431 * A261433 A261434 A261435

Keyword

nonn,easy

Author

Paolo P. Lava, Aug 18 2015

Status

approved