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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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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Invented by the HR concept formation program.
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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
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FORMULA
| f(n) = |{a < n : tau(a)=tau(n)}|
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EXAMPLE
| f(10) = 2 because tau(10)=4 and also tau(6)=tau(8)=4.
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MATHEMATICA
| a[n_] := With[{tau = DivisorSigma[0, n]}, Length[ Select[ Range[n-1], DivisorSigma[0, #] == tau & ]]]; Table[a[n], {n, 1, 87}](* From Jean-François Alcover, Nov 30 2011 *)
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PROG
| (PARI) A047983(n) = {local(d); d=numdiv(n); sum(k=1, n-1, (numdiv(k)==d))} [From Michael B. Porter (michael_b_porter(AT)yahoo.com), Mar 01 2010]
(Haskell)
a047983 n = length [x | x <- [1..n-1], a000005 x == a000005 n]
-- Reihard Zumkeller, Nov 06 2011
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CROSSREFS
| Position of the 0's form A007416. Cf. A005179.
Cf. A000005.
Sequence in context: A124756 A113504 A124754 * A070812 A061865 A135818
Adjacent sequences: A047980 A047981 A047982 * A047984 A047985 A047986
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KEYWORD
| nice,nonn
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AUTHOR
| Simon Colton (simonco(AT)cs.york.ac.uk)
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