A098223 Integer quotients when sigma(sigma(x))/x is an integer.

1, 2, 2, 3, 4, 2, 3, 7, 6, 8, 2, 6, 6, 9, 8, 6, 10, 10, 3, 8, 4, 6, 7, 8, 2, 9, 10, 8, 4, 10, 10, 7, 13, 8, 8, 8, 2, 6, 8, 14, 2, 9, 7, 8, 6, 9, 8, 13, 8, 15, 14, 6, 9, 9, 8, 10, 12, 14, 13, 8, 8, 11, 6, 14, 16, 12, 14, 12, 16, 15, 12, 18, 16, 11, 8, 22

Offset: 1

Author

Labos Elemer, Oct 25 2004

Keywords

• nonn

Comments

Below n=5x10^11, q=5 and 17 quotients do not appear; smallest numbers providing integer quotients = 1, 2, 3, 4,..., 16,... are as follows: 1, 2, 8, 15, ?, 42, 24, 60, 168, 480, 57669920, 2200380, 57120, 217278, 1058148, 7526400, ... - updated by Jud McCranie, Feb 08 2012

The above sequence is now A272930. - Franklin T. Adams-Watters, May 11 2016

See A019278 for the actual numbers x such that x | sigma(sigma(x)). - M. F. Hasler, Jul 03 2016

Links

• Jud McCranie and Giovanni Resta, Table of n, a(n) for n = 1..145 (first 130 terms from Jud McCranie)

Crossrefs

Cf. A000203, A098219-A098222, A019278, A008333, A051027, A272930.

Programs

Maple

with(numtheory): A098223:=n->`if`(sigma(sigma(n)) mod n = 0, sigma(sigma(n))/n, NULL): seq(A098223(n), n=1..10^5); # Wesley Ivan Hurt, Oct 10 2014

Mathematica

Select[DivisorSigma[1, DivisorSigma[1, #]]/# &@ Range[10^6], IntegerQ] (* Michael De Vlieger, May 11 2016 *)

PARI

for(n=1,1e7, sigma(sigma(n))%n||print1(sigma(sigma(n))/n",")) \\ M. F. Hasler, Jul 03 2016

Formula

In order of appearance the sigma(sigma(A019278(n)))/A019278(n) quotients which are by definition integers.