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A047983 Number of integers less than n but with the same number of divisors. 11
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
S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.
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-François 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: A353923 A246370 A362557 * A070812 A308230 A061865
KEYWORD
nice,nonn
AUTHOR
Simon Colton (simonco(AT)cs.york.ac.uk)
STATUS
approved

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Last modified March 19 07:41 EDT 2024. Contains 370958 sequences. (Running on oeis4.)