A079788 -id:A079788 - cp's OEIS frontend

A067004 Number of numbers <= n with same number of divisors as n.

1, 1, 2, 1, 3, 1, 4, 2, 2, 3, 5, 1, 6, 4, 5, 1, 7, 2, 8, 3, 6, 7, 9, 1, 3, 8, 9, 4, 10, 2, 11, 5, 10, 11, 12, 1, 12, 13, 14, 3, 13, 4, 14, 6, 7, 15, 15, 1, 4, 8, 16, 9, 16, 5, 17, 6, 18, 19, 17, 1, 18, 20, 10, 1, 21, 7, 19, 11, 22, 8, 20, 2, 21, 23, 12, 13, 24, 9, 22, 2, 2, 25, 23, 3, 26, 27

Offset: 1

Henry Bottomley, Dec 21 2001

nonn

			a(10)=3 since 6,8,10 each have four divisors. a(11)=5 since 2,3,5,7,11 each have two divisors.

Paul Tek, Table of n, a(n) for n = 1..10000

Cf. A000005, A008479, A058933, A067003. Inverse of A000040, A001248, A030513, A030514, A030515, A030516, A030626, A030627, A030628, A030629, A030630, A030631, A030632, A030633, A030634, A030635, A030636, A030637, A030638 etc.
Cf. also A079788, A138009.
A047983(n) = a(n)-1.

N:= 1000: # to get a(1) to a(N)
R:= Vector(N):
for n from 1 to N do
  v:= numtheory:-tau(n);
  R[v]:= R[v]+1;
  A[n]:= R[v];
od:
seq(A[n],n=1..N); # Robert Israel, May 04 2015

b[_] = 0;
a[n_] := a[n] = With[{t = DivisorSigma[0, n]}, b[t] = b[t]+1];
Array[a, 105] (* Jean-François Alcover, Dec 20 2021 *)

a(n)=my(d=numdiv(n)); sum(k=1,n,numdiv(k)==d) \\ Charles R Greathouse IV, Sep 02 2015

Ordinal transform of A000005. - Franklin T. Adams-Watters, Aug 28 2006

a(A000040(n)^(p-1)) = n if p is prime. - Robert Israel, May 04 2015

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

Original entry on oeis.org

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

Leroy Quet, Feb 27 2008

			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.

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

Cf. A000005, A002182, A067004, A079788.

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

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

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

From Amiram Eldar, Jun 26 2025: (Start)
a(n) = n - 1 if and only if n is prime.
a(n) = 1 if and only if n is a highly composite number (A002182). (End)

More terms from Stefan Steinerberger, Feb 29 2008

cp's OEIS Frontend

A067004 Number of numbers <= n with same number of divisors as n.

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