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Search: id:A131755
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| A131755 |
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a(n) = floor of the average of distances between consecutive positive divisors of n. Also, a(n) = floor((n-1)/(d(n)-1)), where d(n) = A000005(n). |
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1
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| 1, 2, 1, 4, 1, 6, 2, 4, 3, 10, 2, 12, 4, 4, 3, 16, 3, 18, 3, 6, 7, 22, 3, 12, 8, 8, 5, 28, 4, 30, 6, 10, 11, 11, 4, 36, 12, 12, 5, 40, 5, 42, 8, 8, 15, 46, 5, 24, 9, 16, 10, 52, 7, 18, 7, 18, 19, 58, 5, 60, 20, 12, 10, 21, 9, 66, 13, 22, 9, 70, 6, 72, 24, 14, 15, 25, 11, 78, 8
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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(n-1)/(d(n)-1) is an integer if and only if n is in sequence A096738.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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The positive divisors of 12 are 1,2,3,4,6,12. The differences between the pairs of consecutive divisors are 2-1=1, 3-2=1, 4-3=1, 6-4=2, 12-6=6. The average of these differences is (1+1+1+2+6)/5 = 11/5. So a(12) = floor(11/5) = 2.
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MAPLE
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A131755 := proc(n) local dvs ; dvs := sort(convert(numtheory[divisors](n), list)) ; floor(add(op(i, dvs)-op(i-1, dvs), i=2..nops(dvs))/(nops(dvs)-1)) ; end: seq(A131755(n), n=2..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2007
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CROSSREFS
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Cf. A000005, A096738.
Sequence in context: A060794 A074919 A138009 this_sequence A118275 A146938 A147418
Adjacent sequences: A131752 A131753 A131754 this_sequence A131756 A131757 A131758
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Sep 17 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2007
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