

A069901


Smallest prime factor of nth 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
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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.


LINKS



FORMULA

a(4k1) = a(4k) = 2.
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 *)


PROG

(PARI) a(n) = if (n==1, 1, vecmin(factor(n*(n+1)/2)[, 1]));


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



