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).

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, 78, 84, 88, 90, 96, 102, 104, 105, 108, 110, 114, 120, 168, 210, 216, 264, 270, 280, 312, 330, 360, 378, 384, 390, 408, 420, 440, 456, 462, 480, 504, 510, 520, 540, 546, 552, 570, 594, 600, 616

Offset: 1

Author

Vladimir Shevelev, May 13 2016

Keywords

• nonn

Comments

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

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.

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

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037445, A064547, A050376, A067128.

Programs

Mathematica

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-François Alcover at A037445 *)