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A069901 Smallest prime factor of n-th triangular number. +0
6
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; listen)
OFFSET

1,2

COMMENT

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)).

FORMULA

a(4k-1) = a(4k) = 2.

EXAMPLE

A000217(10) = 10*(10+1)/2 = 55 = 5*11, therefore a(10) = 5.

CROSSREFS

Cf. A069902, A069903, A069904.

Sequence in context: A049234 A125504 A075392 this_sequence A115039 A032536 A142246

Adjacent sequences: A069898 A069899 A069900 this_sequence A069902 A069903 A069904

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 10, 2002

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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Last modified March 20 09:10 EDT 2010. Contains 173642 sequences.


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