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Search: id:A066761
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| A066761 |
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Number of positive integers of the form (n^2+k^2)/(n-k) for k=1,2,3,4,....,n-1. |
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3
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| 1, 2, 2, 2, 4, 2, 3, 4, 5, 2, 7, 2, 5, 7, 4, 2, 8, 2, 7, 8, 5, 2, 10, 4, 5, 6, 7, 2, 15, 2, 5, 8, 5, 7, 13, 2, 5, 8, 10, 2, 15, 2, 8, 12, 5, 2, 13, 4, 9, 8, 8, 2, 12, 8, 10, 8, 5, 2, 23, 2, 5, 13, 6, 8, 15, 2, 8, 8, 16, 2, 17, 2, 5, 13, 8, 7, 16, 2, 13, 8, 5, 2, 23, 8, 5, 8, 10, 2, 26, 7, 8, 8, 5, 8
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Also the number of factors of 2*n^2 which are less than n. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 12 2002
Also the number of factors of 2*n^2 which are greater than 2*n, so a(n) = tau(2*n^2)-1-A055081(n). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 13 2002
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FORMULA
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No general formula is known but let k be a positive integer, p and q distinct odd primes then a(2^k)=k a(p^k)=2*k a(p*q)= 7 or 8 if p >13 a(2*p)= 5 if p>5 a(9*p^2)= 23 .... Asymptotic formula : (1/n)*sum(i=1, n, a(i))= ln(n)*ln(ln(n))+o(ln(n))
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EXAMPLE
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a(2)=1 because (2^2+1)/(2-1) is the only integer of this form.
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CROSSREFS
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Sequence in context: A086327 A069930 A114896 this_sequence A108920 A079405 A072048
Adjacent sequences: A066758 A066759 A066760 this_sequence A066762 A066763 A066764
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 17 2002
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EXTENSIONS
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Corrected by Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 12 2002
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