A318166 a(n) begins the first run of at least n consecutive numbers with the same number of infinitary divisors.

1, 2, 2, 2, 32, 141, 141, 141, 42410, 171890, 2648985, 10896843, 10896843, 727940625, 1791416073, 19183907363, 62520703916, 162891847444, 162891847444, 349662337209, 7858045724108

Offset: 1

Author

Amiram Eldar, Aug 20 2018

Keywords

• nonn
• more

Comments

The infinitary version of A006558.

Examples

			a(5) = 32 since the number of infinitary divisors of 32, 33, 34, 35 and 36 is 4, and this is the first run of 5 consecutive numbers.
		

Crossrefs

Cf. A006558, A037445, A045983.

Programs

Mathematica

idivnum[1] = 1; idivnum[n_] := Times @@ Flatten[2^DigitCount[#, 2, 1] & /@ FactorInteger[n][[All, 2]]]; Seq[n_, q_] := Map[idivnum, 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, idivnum[n]]]; n++, {k, nmin, nmax}]; If[found, n - q, 0]]; seq = {1}; nmax = 10000000; Do[n1 = Last[seq]; s1 = findConsec[m, n1, nmax]; If[s1 == 0, Break[]]; AppendTo[seq, s1], {m, 2, 11}];

Extensions

a(12)-a(21) from Giovanni Resta, Aug 24 2018