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A273011 Numbers n such that d_i(n) >= d_i(k) for k = 1 to n-1, where d_i(n) is the number of infinitary divisors of n (A037445). 3

%I

%S 1,2,3,4,5,6,8,10,12,14,15,18,20,21,22,24,30,40,42,54,56,60,66,70,72,

%T 78,84,88,90,96,102,104,105,108,110,114,120,168,210,216,264,270,280,

%U 312,330,360,378,384,390,408,420,440,456,462,480,504,510,520,540,546,552,570,594,600,616

%N Numbers n such that d_i(n) >= d_i(k) for k = 1 to n-1, where d_i(n) is the number of infinitary divisors of n (A037445).

%C An infinitary (or Fermi-Dirac) analog of the Ramanujan sequence A067128.

%C Between the smallest number b_k which is product of k distinct terms of A050376 and b_(k+1) all terms are products of k distinct terms of A050376.

%C Thus every subsequence of terms, having in Fermi-Dirac factorization a fixed number of distinct factors from A050376, is finite.

%C These subsequences have cardinalities: 1, 4, 10, 21, 47, ...

%H Amiram Eldar, <a href="/A273011/b273011.txt">Table of n, a(n) for n = 1..10000</a>

%t a = {}; b = {0}; Do[If[# >= Max@b, AppendTo[a, k] && AppendTo[b, #]] &@ If[k == 1, 1, Times @@ Flatten@ Map[2^First@ DigitCount[#, 2] &, FactorInteger[k][[All, 2]]]], {k, 10^3}]; a (* _Michael De Vlieger_, May 13 2016, after _Jean-Fran├žois Alcover_ at A037445 *)

%Y Cf. A037445, A064547, A050376, A067128.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, May 13 2016

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)