login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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 *)

CROSSREFS

Cf. A037445, A064547, A050376, A067128.

Sequence in context: A162002 A182764 A045880 * A032956 A004272 A004279

Adjacent sequences:  A273008 A273009 A273010 * A273012 A273013 A273014

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, May 13 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)