|
%I #34 Aug 23 2018 17:29:16
%S 1,2,2,2,91,6850,6850,10281,108771,171890,3760204,3760204,727940626,
%T 5704384304,13264434091,13264434091,63719307522,287480681209,
%U 607635436331
%N a(n) begins the first run of at least n consecutive numbers with the same number of bi-unitary divisors.
%C The bi-unitary version of A006558.
%C a(20) > 5*10^12. - _Giovanni Resta_, Aug 23 2018
%e a(5) = 91 since the number of bi-unitary divisors of 91, 92, 93, 94 and 95 is 4, and this is the first run of 5 consecutive numbers.
%t bdivnum[1] = 1; bdivnum[n_] := Times @@ ((# + Mod[#, 2]) & /@ Last /@ FactorInteger[n]); Seq[n_, q_] := Map[bdivnum, Range[n, n + q - 1]]; findConsec[q_, nmin_, nmax_] := Module[{}, s = Seq[1, q]; n = q + 1; found = False; Do[If[CountDistinct[s] == 1, found = True; Break[]]; s = Rest[AppendTo[s, bdivnum[n]]]; n++, {k, nmin, nmax}]; If[found, n - q, 0]]; seq = {1}; nmax = 100000000; Do[n1 = Last[seq]; s1 = findConsec[m, n1, nmax]; If[s1 == 0, Break[]]; AppendTo[seq, s1], {m, 2, 13}];
%Y Cf. A006558, A045983 (equivalent for unitary divisors), A286324.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Aug 20 2018
%E a(14)-a(19) from _Giovanni Resta_, Aug 23 2018
|
