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A047983
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Number of integers less than n but with the same number of divisors.
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11
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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
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1,5
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COMMENTS
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Invented by the HR concept formation program.
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LINKS
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FORMULA
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f(n) = |{a < n : tau(a)=tau(n)}|.
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EXAMPLE
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f(10) = 2 because tau(10)=4 and also tau(6)=tau(8)=4.
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a047983 n = length [x | x <- [1..n-1], a000005 x == a000005 n]
(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
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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Simon Colton (simonco(AT)cs.york.ac.uk)
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STATUS
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approved
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