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 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. 7
 1, 2, 8, 15 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified May 30 19:06 EDT 2020. Contains 334729 sequences. (Running on oeis4.)