A304463 a(n) begins the first run of at least n consecutive numbers with the same number of bi-unitary divisors.

1, 2, 2, 2, 91, 6850, 6850, 10281, 108771, 171890, 3760204, 3760204, 727940626, 5704384304, 13264434091, 13264434091, 63719307522, 287480681209, 607635436331

Offset: 1

Author

Amiram Eldar, Aug 20 2018

Keywords

• nonn
• more

Comments

The bi-unitary version of A006558.

a(20) > 5*10^12. - Giovanni Resta, Aug 23 2018

Examples

			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.
		

Crossrefs

Cf. A006558, A045983 (equivalent for unitary divisors), A286324.

Programs

Mathematica

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}];

Extensions

a(14)-a(19) from Giovanni Resta, Aug 23 2018