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 A115411 a(n) = least k such that semiprime(n) divides k-th triangular number. 0

%I

%S 7,3,8,4,7,5,6,11,24,12,11,16,14,19,12,23,48,17,10,18,28,31,25,23,36,

%T 21,40,34,43,29,13,30,47,19,52,36,45,59,34,120,60,41,42,56,67,47,71,

%U 65,29,72,30,79,53,69,83,168,59,88,60,74,33,96,66,100,28,40,103,76,71,107,85

%N a(n) = least k such that semiprime(n) divides k-th triangular number.

%C a(n) = MIN[k such that A001358(n) | A000217(k)].

%e a(1) = 7 because SP(1) = semiprime(1) = 4, Triangular number T(7) = 7*(7+1)/2 = 28 and 7 divides 28.

%e a(2) = 3 because SP(2) = 6 | T(3) = 6.

%e a(3) = 8 because SP(3) = 9 | T(8) = 36.

%e a(9) = 24 because SP(9) = 25 | T(24) = 300.

%e a(17) = 48 because SP(17) = 49 | T(48) = 1176.

%t a = Select[Range@215, Plus @@ Last /@ FactorInteger@# == 2 &]; f[n_] := Block[{k = 1}, While[ Mod[k(k + 1)/2, a[[n]]] > 0, k++ ]; k]; Array[f, 71] (* Robert G. Wilson v *)

%Y Cf. A000217, A001358.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Mar 08 2006

%E More terms from _Robert G. Wilson v_, May 01 2006

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