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Search: id:A060789
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| A060789 |
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a(n) = n / (gcd(n,2) * gcd(n,3)). |
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+0
6
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| 1, 1, 1, 2, 5, 1, 7, 4, 3, 5, 11, 2, 13, 7, 5, 8, 17, 3, 19, 10, 7, 11, 23, 4, 25, 13, 9, 14, 29, 5, 31, 16, 11, 17, 35, 6, 37, 19, 13, 20, 41, 7, 43, 22, 15, 23, 47, 8, 49, 25, 17, 26, 53, 9, 55, 28, 19, 29, 59, 10, 61, 31, 21, 32, 65, 11, 67, 34, 23, 35, 71, 12, 73, 37, 25, 38, 77
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n+2) is absolute value of numerator of determinant of n X n matrix with M(i,j) = 2/(i(i+1)) if i=j otherwise 1. - Alexander Adamchuk (alex(AT)kolmogorov.com), May 19 2006
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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G.f.: (x + x^2 + x^3 + 2x^4 + 5x^5 + x^6 + 5x^7 + 2x^8 + x^9 + x^10 + x^11)/(x^6 - 1)^2.
Multiplicative with a(2^e)=2^(e-1), a(3^e)=3^(e-1), a(p^e)=p^e, p>3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 09 2004
a(n) = Numerator[(-1)^(n+1)*Det[DiagonalMatrix[Table[2/(i(i+1))-1, {i,1,n-2}]]+1]], n>2. - Alexander Adamchuk (alex(AT)kolmogorov.com), May 19 2006
a(n) divides n. a(6k) = k for integer k>0. a(p^k) = p^k for prime p>3 and integerk>0. - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 20 2006
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MATHEMATICA
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Numerator[Table[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ 2/(i(i+1)) - 1, {i, 1, n-2} ] ] + 1 ], {n, 1, 30} ]] - Alexander Adamchuk (alex(AT)kolmogorov.com), May 19 2006
Table[Numerator[(n+3)/(n+2)/(n+1)/n], {n, 60}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 17 2009]
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PROGRAM
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(Other) sage: [lcm(n, 6)/6for n in xrange(1, 78)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2009]
(PARI) { for (n=1, 1000, write("b060789.txt", n, " ", n / (gcd(n, 2) * gcd(n, 3))); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 11 2009]
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CROSSREFS
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Sequence in context: A065224 A165278 A106619 this_sequence A134570 A019510 A124576
Adjacent sequences: A060786 A060787 A060788 this_sequence A060790 A060791 A060792
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KEYWORD
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nonn,easy,mult,new
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AUTHOR
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Len Smiley (smiley(AT)math.uaa.alaska.edu), Apr 26 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001
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