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A011772
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Smallest number m such that m(m+1)/2 is divisible by n.
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10
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1, 3, 2, 7, 4, 3, 6, 15, 8, 4, 10, 8, 12, 7, 5, 31, 16, 8, 18, 15, 6, 11, 22, 15, 24, 12, 26, 7, 28, 15, 30, 63, 11, 16, 14, 8, 36, 19, 12, 15, 40, 20, 42, 32, 9, 23, 46, 32, 48, 24, 17, 39, 52, 27, 10, 48, 18, 28, 58, 15, 60, 31, 27, 127, 25, 11, 66, 16, 23, 20, 70, 63, 72, 36, 24
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also called pseudo-Smarandache numbers.
a(2^k) = 2^(k+1)-1; a(m)=m-1 and for odd prime powers m; - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 26 2003
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REFERENCES
| C. Ashbacher, The Pseudo-Smarandache Function and the Classical Functions of Number Theory, Smarandache Notions Journal, Vol. 9, No. 1-2, 1998, 79-82.
K. Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus University Press, 1996.
K. Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus Univ. Press, 1996.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
M. L. Perez et al., eds., Smarandache Notions Journal
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
K. Kashihara, Comments and Topics on Smarandache Notions and Problems.
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FORMULA
| a(n) <= 2n-1 for all numbers n; a(n) <= n-1 for odd n - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 03 2006
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MATHEMATICA
| Table[m := 1; While[Not[IntegerQ[(m*(m + 1))/(2n)]], m++ ]; m, {n, 1, 90}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 03 2006
(Sqrt[1+8#]-1)/2&/@Flatten[With[{r=Accumulate[Range[300]]}, Table[ Select[r, Divisible[#, n]&, 1], {n, 80}]]] (* From Harvey P. Dale, Feb 05 2012 *)
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CROSSREFS
| A066561(n)=A000217(a(n)).
Cf. A080982.
Sequence in context: A075270 A067872 A198501 * A060451 A129187 A166532
Adjacent sequences: A011769 A011770 A011771 * A011773 A011774 A011775
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KEYWORD
| nonn,easy,nice,changed
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AUTHOR
| Kenichiro Kashihara (Univxiq(AT)aol.com)
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 03 2006
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