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

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, 21, 40, 34, 43, 29, 13, 30, 47, 19, 52, 36, 45, 59, 34, 120, 60, 41, 42, 56, 67, 47, 71, 65, 29, 72, 30, 79, 53, 69, 83, 168, 59, 88, 60, 74, 33, 96, 66, 100, 28, 40, 103, 76, 71, 107, 85

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..71.

Example

a(1) = 7 because SP(1) = semiprime(1) = 4, Triangular number T(7) = 7*(7+1)/2 = 28 and 7 divides 28.
a(2) = 3 because SP(2) = 6 | T(3) = 6.
a(3) = 8 because SP(3) = 9 | T(8) = 36.
a(9) = 24 because SP(9) = 25 | T(24) = 300.
a(17) = 48 because SP(17) = 49 | T(48) = 1176.

Mathematica

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 *)

Crossrefs

Cf. A000217, A001358.

Sequence in context: A111197 A245645 A335994 * A019726 A011330 A093587

Adjacent sequences: A115408 A115409 A115410 * A115412 A115413 A115414

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 08 2006

Extensions

More terms from Robert G. Wilson v, May 01 2006

Status

approved