A226442 a(n) = smallest index m such that smallest prime factor of m-th triangular number is prime(n).

3, 2, 10, 13, 22, 298, 526, 37, 46, 58, 61, 73, 82, 3397, 2866, 106, 3481, 3721, 5293, 5041, 7081, 157, 166, 178, 193, 10201, 14317, 23326, 23761, 226, 17398, 262, 19042, 277, 24286, 38806, 313, 45802, 29893, 346, 358, 32761, 382, 46126, 52993, 397, 421, 68461

Offset: 1

Author

Zak Seidov, Jun 06 2013

Keywords

• nonn

Comments

Or, smallest proper divisor of m-th triangular number is prime(n).

The curve is bimodal. Why? - T. D. Noe, Jun 07 2013

Examples

			3rd triangular number, A000217(3) = 6 = 2*3, 2nd triangular number, A000217(2) = 3,
10th triangular number, A000217(10) = 55 = 5*11, 13th triangular number, A000217(13) = 91 =7*13.
		

Crossrefs

Cf. A000040, A000217, A069901.

Programs

Mathematica

nn = 50; t = Table[0, {nn}]; tri = 1; n = 1; found = 0; While[found < nn, n++; tri = tri + n; p = FactorInteger[tri][[1, 1]]; pi = PrimePi[p]; If[pi <= nn && t[[pi]] == 0, t[[pi]] = n; found++]]; t (* T. D. Noe, Jun 07 2013 *)

Formula

A069901(a(n)) = A000040(n).