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Search: id:A086886
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| A086886 |
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Ljungstrand's sequence: number of unique solutions to n = (X + 1/x)(Y + 1/y), where x,y>1 and X,Y are integers. |
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+0
1
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| 0, 1, 2, 3, 4, 5, 5, 6, 8, 8, 8, 9, 8, 10, 14, 12, 10, 11, 10, 14, 17, 14, 13, 16, 18, 13, 17, 21, 13, 19, 12, 14, 23, 16, 26, 26, 14, 17, 21, 26, 16, 23, 16, 22, 30, 22, 18, 22, 24, 22, 26, 23, 18, 28, 33, 32, 29, 21, 20, 32, 19, 19, 30, 30, 35, 27, 18, 28, 31, 41, 20, 33, 19
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) < n, and lim{n->inf, Sum[k=1..n, a(k)] / (n*log(n)^3) } = 3/(2Pi^2) (see article).
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LINKS
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J. Brzezinski, W. Holsztynski and P. Kurlberg, On the congruence ax+by=1 modulo xy
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PROGRAM
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(PARI) w(n)=ant=0; fordiv(n, a, for(X=1, floor(sqrt(n)), fordiv(a+X, k, if(gcd(n-k, X)!=X||gcd(n/a+(n-k)/X, k)!=k, next); Y=(n-k)/X; x=(n/a+(n-k)/X)/k; y=(a+X)/k; if(x==1||y==1, next); if(X==Y, ant=ant+1/2, ant=ant+1)))); ant (from Juliusz Brzezinski)
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CROSSREFS
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Sequence in context: A029915 A108141 A017866 this_sequence A017840 A017855 A051598
Adjacent sequences: A086883 A086884 A086885 this_sequence A086887 A086888 A086889
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 22, 2003; revised Dec 08 2004
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