A074786 Numbers k such that phi(k) = Sum_{d|k} core(d) where core(x) is the squarefree part of x (A007913).

1, 99, 1080, 1836, 4743, 5670, 7644, 8307, 14384, 14784, 15225, 15824, 16065, 20300, 21584, 25704, 29760, 34544, 46816, 71568, 94240, 128412, 169290, 264160, 266266, 312480, 331731, 364941, 404550, 445050, 454575, 458052, 479655, 497781

Offset: 1

Author

Benoit Cloitre, Sep 07 2002

Keywords

• nonn

Comments

Numbers k such that A000010(k) = A069088(k). - Amiram Eldar, Apr 28 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..500 from Donovan Johnson)

Crossrefs

Cf. A000010, A007913, A069088.

Programs

Mathematica

f[p_, e_] := If[OddQ[e], (p+1)*(e+1)/2, (p+1)*e/2 + 1] / ((p-1)*p^(e-1)); q[1] = True; q[n_] := Times @@ f @@@ FactorInteger[n] == 1; Select[Range[500000], q] (* Amiram Eldar, Apr 28 2025 *)

PARI

isok(n) = eulerphi(n) == sumdiv(n, d, core(d)); \\ Michel Marcus, Aug 09 2013

PARI

isok(k) = {my(f = factor(k)); prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; if(e % 2, (p+1)*(e+1)/2, (p+1)*e/2 + 1) / ((p-1)*p^(e-1))) == 1;} \\ Amiram Eldar, Apr 28 2025

Extensions

More terms from Michel Marcus, Aug 09 2013