A272930 a(n) is the least k such that sigma(sigma(k)) = n*k, where sigma(n) is the sum of the divisors of n, or 0 if no such k exists.

1, 2, 8, 15

Offset

1,2

Comments

If a(5) is not zero, it exceeds 5*10^11 (see A098223). Likewise for a(17).

a(6) to a(16) are 42, 24, 60, 168, 480, 4404480, 2200380, 57120, 217728, 1058148, 7526400. a(18) is 39352320.

Is a(n) in fact nonzero for every positive n? - Franklin T. Adams-Watters, Jan 22 2019 [who previously conjectured that it is]

a(19) to a(26) are 312792480, 1505806848, 341543854080, 83825280, 13460388480, 8530704000, 58350015360, 284430182400. - Michel Marcus, May 18 2016

From Michel Marcus, May 18 2016; Jul 19 2016, Aug 23 2016, Sep 06 2016: (Start)

a(17) <= 336421458837032140800;

a(27) <= 4641476998878720;

a(28) <= 23479734980782080;

a(29) <= 4670834235654671884800;

a(30) <= 7526652811748265000960;

a(31) <= 45781120625942782080;

a(32) <= 242094947364010540800;

a(33) <= 216462850095065333760000;

a(34) <= 2366077977040955880819916800;

a(35) <= 8076837429313362044375040000;

a(36) <= 2634106558176405916291008921600;

a(37) <= 299500004890186577026355605378405509365760000000;

a(38) <= 45103591381041833364829469933568000. (End)

Links

Table of n, a(n) for n=1..4.

See the links in A019278. - Altug Alkan, May 31 2016 and May 18 2016

Example

sigma(8) = 15. sigma(15) = 24 = 3*8. Since this does not work for any value smaller than 8, a(3) = 8.

Maple

with(numtheory):
a:=proc(n) local k :
for k while sigma(sigma(k))<>n*k do od : k end: # Robert FERREOL, Apr 11 2018

Mathematica

Table[SelectFirst[Range[10^2], Nest[DivisorSigma[1, #] &, #, 2] == n # &], {n, 4}] (* Michael De Vlieger, May 11 2016, Version 10 *)

Prog

(PARI) a(n)=my(r=1); while(sigma(sigma(r))!=n*r, r++); r \\ works only if a(n) is not zero.

Crossrefs

Cf. A000203 (sigma), A098223, A051027, A019279, A007539, A019278.

Sequence in context: A192777 A054981 A059449 * A140973 A065907 A031272

Adjacent sequences: A272927 A272928 A272929 * A272931 A272932 A272933

Keyword

nonn,more,bref

Author

Franklin T. Adams-Watters, May 11 2016

Status

approved