

A273011


Numbers n such that d_i(n) >= d_i(k) for k = 1 to n1, 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 FermiDirac) 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 FermiDirac 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 JeanFrançois Alcover at A037445 *)


CROSSREFS

Cf. A037445, A064547, A050376, A067128.
Sequence in context: A090811 A162002 A182764 * A032956 A004272 A004279
Adjacent sequences: A273008 A273009 A273010 * A273012 A273013 A273014


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, May 13 2016


STATUS

approved



