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A069901 Smallest prime factor of n-th triangular number. 7
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; text; internal format)
OFFSET

1,2

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, 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)).

LINKS

Zak Seidov, Table of n, a(n) for n = 1..10000

FORMULA

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

From Zak Seidov, Jun 06 2013: (Start)

a(n) = 3 for n = {2, 5, 6, 9} + 12 k;

a(n) = 5 for n = {10, 25, 34, 49} + 60 k;

a(n) = 7 for n = {13, 97, 118, 133, 181, 202, 217, 238, 286, 301, 322, 406} + 420 k, etc. (end)

EXAMPLE

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

MATHEMATICA

FactorInteger[#][[1, 1]]&/@Accumulate[Range[100]] (* Harvey P. Dale, Apr 05 2014 *)

CROSSREFS

Cf. A069902, A069903, A069904.

Sequence in context: A125504 A243929 A075392 * A115039 A032536 A115061

Adjacent sequences:  A069898 A069899 A069900 * A069902 A069903 A069904

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 10, 2002

EXTENSIONS

Edited by N. J. A. Sloane, Sep 06 2008 at the suggestion of Franklin T. Adams-Watters

STATUS

approved

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Last modified January 20 11:11 EST 2020. Contains 331083 sequences. (Running on oeis4.)