login
A318166
a(n) begins the first run of at least n consecutive numbers with the same number of infinitary divisors.
4
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.
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
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Aug 20 2018
EXTENSIONS
a(12)-a(21) from Giovanni Resta, Aug 24 2018
STATUS
approved