A062823 - OEIS

A062823

Numbers k such that the number of divisors of k divides the number of divisors of the totient of k.

1, 3, 7, 11, 13, 14, 15, 19, 22, 23, 25, 28, 29, 31, 35, 39, 41, 43, 44, 46, 47, 50, 53, 55, 56, 59, 61, 62, 67, 68, 70, 71, 73, 77, 78, 79, 82, 83, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 103, 107, 109, 110, 111, 112, 113, 115, 117, 118, 119, 122, 124, 127, 129, 131

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1001 from Harry J. Smith)

EXAMPLE

For k = {3,11,29}, phi(k) = {2,10,28}, d(phi(k)) = {2,4,6}, d(k) = 2, quotient = {1,2,3}.

MATHEMATICA

Select[Range@ 132, Mod @@ DivisorSigma[0, {EulerPhi@ #, #}] == 0 &] (* Michael De Vlieger, Jun 29 2018 *)

PROG

(PARI) select(m->frac(numdiv(eulerphi(m))/numdiv(m)) == 0, [1..500]) \\ Harry J. Smith, Aug 11 2009

(PARI) isok(k) = {my(f = factor(k)); !(numdiv(eulerphi(f)) % numdiv(f)); } \\ Amiram Eldar, Jan 31 2025

CROSSREFS

Cf. A000005, A000010, A062821.

Sequence in context: A055050 A096346 A104534 * A031466 A045062 A111068

Adjacent sequences: A062820 A062821 A062822 * A062824 A062825 A062826

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 20 2001

EXTENSIONS

Incorrect formula deleted by Jon E. Schoenfield, Jul 02 2018

Offset corrected by Amiram Eldar, Jan 31 2025

STATUS

approved