

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
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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[n1], DivisorSigma[0, #] == tau & ]]]; Table[a[n], {n, 1, 87}](* JeanFrançois 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, n1, (numdiv(k)==d))} \\ Michael B. Porter, Mar 01 2010
(Haskell)
a047983 n = length [x  x < [1..n1], 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



