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A069901
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Smallest prime factor of n-th triangular number.
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5
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1, 3, 2, 2, 3, 3, 2, 2, 3, 5, 2, 2, 7, 3, 2, 2, 3, 3, 2, 2, 3, 11, 2, 2, 5, 3, 2, 2, 3, 3, 2, 2, 3, 5, 2, 2, 19, 3, 2, 2, 3, 3, 2, 2, 3, 23, 2, 2, 5, 3, 2, 2, 3, 3, 2, 2, 3, 29, 2, 2, 31, 3, 2, 2, 3, 3, 2, 2, 3, 5, 2, 2, 37, 3, 2, 2, 3, 3, 2, 2, 3, 41, 2, 2, 5, 3, 2, 2, 3, 3, 2, 2, 3, 5, 2, 2, 7, 3, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Or, a(1) = 1, then the smallest nontrivial k (>1) which divides the sum of (next n) numbers from k+1 to k+n or smallest k > 1 that divides nk + n(n+1)/2. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 22 2002. For example, a(7) = 4, which is the smallest nontrivial number that divides the sum 5+6+...+11, of 7 numbers.
a(n) = A020639(A000217(n)).
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FORMULA
| a(4k-1) = a(4k) = 2.
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EXAMPLE
| A000217(10) = 10*(10+1)/2 = 55 = 5*11, therefore a(10) = 5.
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CROSSREFS
| Cf. A069902, A069903, A069904.
Sequence in context: A049234 A125504 A075392 * A115039 A032536 A115061
Adjacent sequences: A069898 A069899 A069900 * A069902 A069903 A069904
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 10, 2002
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 06 2008 at the suggestion of Franklin T. Adams-Watters
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