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
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
KEYWORD
nonn,more,bref
AUTHOR
Franklin T. Adams-Watters, May 11 2016
STATUS
approved