

A138009


a(n) = number of positive integers k, k <= n, where d(k) >= d(n); d(n) = number of positive divisors of n.


3



1, 1, 2, 1, 4, 1, 6, 2, 4, 3, 10, 1, 12, 5, 6, 2, 16, 2, 18, 3, 10, 11, 22, 1, 15, 13, 14, 5, 28, 2, 30, 7, 18, 19, 20, 1, 36, 22, 23, 4, 40, 5, 42, 11, 12, 28, 46, 1, 33, 14, 31, 15, 52, 7, 34, 8, 36, 37, 58, 1, 60, 39, 19, 10, 42, 10, 66, 22, 45, 11, 70, 2, 72, 48, 25, 26, 51, 13, 78, 4
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OFFSET

1,3


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

9 has 3 positive divisors. Among the first 9 positive integers, there are four that have more than or equal the number of divisors than 9 has: 4, with 3 divisors; 6, with 4 divisors; 8, with 4 divisors; and 9, with 3 divisors. So a(9) = 4.


MAPLE

L:= [2]: A[1]:= 1:
for n from 2 to 100 do
v:= 2*numtheory:tau(n);
k:= ListTools:BinaryPlace(L, v1);
A[n]:= nk;
L:= [op(L[1..k]), v, op(L[k+1..1])];
od:
seq(A[i], i=1..100); # Robert Israel, Sep 26 2018


MATHEMATICA

Table[Length[Select[Range[n], Length[Divisors[ # ]]>=Length[Divisors[n]]&]], {n, 1, 100}] (* Stefan Steinerberger, Feb 29 2008 *)


PROG

(PARI) a(n) = my(dn=numdiv(n)); sum(k=1, n, numdiv(k) >= dn); \\ Michel Marcus, Sep 26 2018


CROSSREFS

Cf. A079788, A067004.
Sequence in context: A060794 A300716 A074919 * A131755 A305812 A341857
Adjacent sequences: A138006 A138007 A138008 * A138010 A138011 A138012


KEYWORD

nonn,look


AUTHOR

Leroy Quet, Feb 27 2008


EXTENSIONS

More terms from Stefan Steinerberger, Feb 29 2008


STATUS

approved



