login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047983 Number of integers less than n but with the same number of divisors. 3
0, 0, 1, 0, 2, 0, 3, 1, 1, 2, 4, 0, 5, 3, 4, 0, 6, 1, 7, 2, 5, 6, 8, 0, 2, 7, 8, 3, 9, 1, 10, 4, 9, 10, 11, 0, 11, 12, 13, 2, 12, 3, 13, 5, 6, 14, 14, 0, 3, 7, 15, 8, 15, 4, 16, 5, 17, 18, 16, 0, 17, 19, 9, 0, 20, 6, 18, 10, 21, 7, 19, 1, 20, 22, 11, 12, 23, 8, 21, 1, 1, 24, 22, 2, 25, 26, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Invented by the HR concept formation program.

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000

S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.

S. Colton, HR - Automatic Theory Formation in Pure Mathematics

FORMULA

f(n) = |{a < n : tau(a)=tau(n)}|

EXAMPLE

f(10) = 2 because tau(10)=4 and also tau(6)=tau(8)=4.

MATHEMATICA

a[n_] := With[{tau = DivisorSigma[0, n]}, Length[ Select[ Range[n-1], DivisorSigma[0, #] == tau & ]]]; Table[a[n], {n, 1, 87}](* Jean-Fran├žois Alcover, Nov 30 2011 *)

Module[{nn=90, ds}, ds=DivisorSigma[0, Range[nn]]; Table[Count[Take[ds, n], ds[[n]]]- 1, {n, nn}]] (* Harvey P. Dale, Feb 16 2014 *)

PROG

(PARI) A047983(n) = {local(d); d=numdiv(n); sum(k=1, n-1, (numdiv(k)==d))} \\ Michael B. Porter, Mar 01 2010

(Haskell)

a047983 n = length [x | x <- [1..n-1], a000005 x == a000005 n]

-- Reinhard Zumkeller, Nov 06 2011

(Python)

from sympy import divisor_count as D

def a(n): return sum([1 for k in range(1, n) if D(k) == D(n)]) # Indranil Ghosh, Apr 30 2017

CROSSREFS

Position of the 0's form A007416. Cf. A005179.

Cf. A000005.

Sequence in context: A276165 A124754 A246370 * A070812 A308230 A061865

Adjacent sequences:  A047980 A047981 A047982 * A047984 A047985 A047986

KEYWORD

nice,nonn

AUTHOR

Simon Colton (simonco(AT)cs.york.ac.uk)

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 3 19:43 EDT 2020. Contains 333198 sequences. (Running on oeis4.)