A138009 a(n) = number of positive integers k, k <= n, where d(k) >= d(n); d(n) = number of positive divisors of n.

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

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, v-1);
  A[n]:= n-k;
  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: A300716 A074919 A362232 * 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