A069552 Numbers k such that phi(k) = sigma(core(k)) where phi(k) is the Euler totient function, sigma(k) the sum of divisors of k and core(k) the squarefree part of k (the smallest integer such that k*core(k) is a square).

1, 12, 56, 140, 270, 630, 1672, 4180, 6426, 18810, 80104, 93496, 99484, 102856, 116116, 140296, 191862, 200260, 220616, 223938, 224536, 233740, 257140, 350740, 447678, 449442, 522522, 551540, 561340, 702240, 901170, 1051830, 1157130, 1578330, 2481930, 2526030

Offset

1,2

Comments

phi(k) = sigma(core(k)) | sigma(k) so this is a subsequence of A020492. - David A. Corneth, Sep 08 2020

Links

David A. Corneth, Table of n, a(n) for n = 1..16559 (first 183 terms from Amiram Eldar, terms calculated from terms provided by Jud McCranie in A020492)

Example

140 is in the sequence as phi(140) = 48 = sigma(35) = sigma(core(140)). - David A. Corneth, Sep 08 2020

Mathematica

core[n_] := Times @@ Power @@@ ({#[[1]], Mod[ #[[2]], 2]} & /@ FactorInteger[n]); Select[Range[10^5], EulerPhi[#] == DivisorSigma[1, core[#]] &] (* Amiram Eldar, Jul 11 2019 after Zak Seidov at A007913 *)

Prog

(PARI) for(n=1, 10^6, if(eulerphi(n)==sigma(core(n)), print1(n, ", ")))

Crossrefs

Cf. A000010, A000203, A007913, A020492.

Sequence in context: A133001 A340517 A104188 * A035005 A001386 A046998

Adjacent sequences: A069549 A069550 A069551 * A069553 A069554 A069555

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 17 2002

Extensions

More terms from Amiram Eldar, Jul 11 2019

Status

approved