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A135376 a(n) = the smallest prime that does not divide n(n+1)/2. 1
2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 5, 5, 2, 2, 7, 3, 2, 2, 3, 11, 2, 2, 5, 7, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 11, 5, 2, 2, 7, 3, 2, 2, 3, 7, 2, 2, 5, 5, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 7, 7, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 5, 5, 2, 2, 7, 3, 2, 2, 3, 7, 2, 2, 5, 11, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 7, 5, 2, 2, 7, 3, 2, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(4n+1) = a(4n+2) = 2 for all nonnegative integers n. a(n) = A053670(n) for all n congruent to 0 or 3 (mod 4).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A053669(A000217(n)). - R. J. Mathar, Dec 11 2007

EXAMPLE

The 11th triangular number is 66 = 2*3*11. 5 is the smallest prime that is coprime to 66, so a(11) = 5.

MAPLE

A135376 := proc(n) local T, p ; T := n*(n+1)/2 ; p := 2 ; while T mod p = 0 do p := nextprime(p) ; od: RETURN(p) ; end: seq(A135376(n), n=1..120) ; # R. J. Mathar, Dec 11 2007

MATHEMATICA

a = {}; For[n = 1, n < 80, n++, j = 1; While[Mod[n*(n + 1)/2, Prime[j]] == 0, j++ ]; AppendTo[a, Prime[j]]]; a (* Stefan Steinerberger, Dec 10 2007 *)

sp[n_]:=Module[{p=2}, While[Mod[n, p]==0, p=NextPrime[p]]; p]; sp[#]&/@ Accumulate[ Range[110]] (* Harvey P. Dale, Jul 26 2018 *)

CROSSREFS

Cf. A053670.

Sequence in context: A197591 A097891 A097611 * A132850 A076561 A132851

Adjacent sequences:  A135373 A135374 A135375 * A135377 A135378 A135379

KEYWORD

nonn

AUTHOR

Leroy Quet, Dec 09 2007

EXTENSIONS

More terms from Stefan Steinerberger and R. J. Mathar, Dec 10 2007

STATUS

approved

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Last modified April 1 14:52 EDT 2020. Contains 333163 sequences. (Running on oeis4.)