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A226442
a(n) = smallest index m such that smallest prime factor of m-th triangular number is prime(n).
0
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
1,1
COMMENTS
Or, smallest proper divisor of m-th triangular number is prime(n).
The curve is bimodal. Why? - T. D. Noe, Jun 07 2013
FORMULA
A069901(a(n)) = A000040(n).
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Jun 06 2013
STATUS
approved