A318166 - OEIS

%I #15 Aug 24 2018 04:54:26

%S 1,2,2,2,32,141,141,141,42410,171890,2648985,10896843,10896843,

%T 727940625,1791416073,19183907363,62520703916,162891847444,

%U 162891847444,349662337209,7858045724108

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

%C The infinitary version of A006558.

%e 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.

%t 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}];

%Y Cf. A006558, A037445, A045983.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Aug 20 2018

%E a(12)-a(21) from _Giovanni Resta_, Aug 24 2018