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Search: id:A060794
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| A060794 |
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Difference between upper and lower central divisors of n. |
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+0
1
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| 1, 2, 1, 4, 1, 6, 2, 2, 3, 10, 1, 12, 5, 2, 2, 16, 3, 18, 1, 4, 9, 22, 2, 4, 11, 6, 3, 28, 1, 30, 4, 8, 15, 2, 2, 36, 17, 10, 3, 40, 1, 42, 7, 4, 21, 46, 2, 6, 5, 14, 9, 52, 3, 6, 1, 16, 27, 58, 4, 60, 29, 2, 4, 8, 5, 66, 13, 20, 3, 70, 1, 72, 35, 10, 15, 4, 7, 78, 2, 6, 39, 82, 5, 12, 41, 26
(list; graph; listen)
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OFFSET
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2,2
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LINKS
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Harry J. Smith, Table of n, a(n) for n=2,...,1000
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EXAMPLE
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Difference between upper and lower central divisors may be small or relatively large. So neither A060775 nor A033677 are always good central divisors as to their magnitude. n=182,D={1,2,7,13,14,26,91,182}; central divisors={13,14}, difference=1. n=254, D={1,2,127,254}, central divisors={2,127}, a(254)=125. n=p, D={1,p}. Here the central divisors are also marginal ones: a(p)=p-1.
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MATHEMATICA
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a(n)=Part[Divisors[n], 1+cd[n]]-Part[Divisors[n], cd[n]], where cd[x_] := cd[x_] := Floor[DivisorSigma[0, x]/2]
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PROGRAM
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(PARI) { for (n=2, 1000, d=divisors(n); write("b060794.txt", n, " ", d[1 + length(d)\2] - d[length(d)\2]); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 12 2009]
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CROSSREFS
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a(n)=A033677(n)-A060775(n).
Cf. A060775-A060777, A033677, A000196.
Sequence in context: A147064 A147228 A074643 this_sequence A074919 A138009 A131755
Adjacent sequences: A060791 A060792 A060793 this_sequence A060795 A060796 A060797
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Apr 27 2001
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