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

1,3

Links

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

Formula

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

Example

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

Maple

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

Mathematica

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 *)

Prog

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

Crossrefs

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.

Sequence in context: A338565 A323638 A249336 * A117920 A378646 A079617

Adjacent sequences: A067001 A067002 A067003 * A067005 A067006 A067007

Keyword

nonn

Author

Henry Bottomley, Dec 21 2001

Status

approved