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

1,2

Comments

The infinitary version of A006558.

Links

Table of n, a(n) for n=1..21.

Example

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.

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}];

Crossrefs

Cf. A006558, A037445, A045983.

Sequence in context: A147975 A083148 A368204 * A241845 A254131 A339014

Adjacent sequences: A318163 A318164 A318165 * A318167 A318168 A318169

Keyword

nonn,more

Author

Amiram Eldar, Aug 20 2018

Extensions

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

Status

approved