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Search: id:A078181
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| A078181 |
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Sum_{d|n, d=1 mod 3} d. |
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+0
7
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| 1, 1, 1, 5, 1, 1, 8, 5, 1, 11, 1, 5, 14, 8, 1, 21, 1, 1, 20, 15, 8, 23, 1, 5, 26, 14, 1, 40, 1, 11, 32, 21, 1, 35, 8, 5, 38, 20, 14, 55, 1, 8, 44, 27, 1, 47, 1, 21, 57, 36, 1, 70, 1, 1, 56, 40, 20, 59, 1, 15, 62, 32, 8, 85, 14, 23, 68, 39, 1, 88, 1, 5, 74, 38, 26, 100, 8, 14, 80, 71, 1
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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G.f.: Sum_{n>=0} (3*n+1)*x^(3*n+1)/(1-x^(3*n+1)).
Conjecture. If a(n)=n+1 then n==1 (mod 3). (Is this easy to settle? It has been verified for n=1,2,3,...,2000.) - John W. Layman (layman(AT)math.vt.edu), Apr 03 2006
The conjecture is false. The first and only counterexample below 10^8 is a(6800)=6801 and 6800=2 mod 3. - Lambert Herrgesell (zero815(AT)googlemail.com), May 06 2008
Equals A051731 * [1, 0, 0, 4, 0, 0, 7, 0, 0, 10,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 06 2007
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CROSSREFS
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Cf. A001817, A001822, A078181, A051731.
Sequence in context: A132737 A137754 A131404 this_sequence A054110 A132048 A141398
Adjacent sequences: A078178 A078179 A078180 this_sequence A078182 A078183 A078184
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 21 2002
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