A085779 Smallest m such that the triangular number A000217(n) divides m!.

1, 3, 3, 5, 5, 7, 7, 6, 6, 11, 11, 13, 13, 7, 5, 17, 17, 19, 19, 7, 11, 23, 23, 10, 13, 13, 9, 29, 29, 31, 31, 11, 17, 17, 7, 37, 37, 19, 13, 41, 41, 43, 43, 11, 23, 47, 47, 14, 14, 17, 17, 53, 53, 11, 11, 19, 29, 59, 59, 61, 61, 31, 8, 13, 13, 67, 67, 23, 23, 71, 71, 73, 73, 37, 19, 19

Offset: 1

Author

Jon Perry, Jul 23 2003

Keywords

• nonn

Examples

			t(4) = 10 and the first factorial divisible by 10 is 5!, so a(4) = 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A002034.

Programs

Mathematica

nn=80;With[{f=Range[nn]!,trs=Accumulate[Range[nn]]},Flatten[ Table[ Position[f,?(Divisible[#,trs[[n]]]&),{1},1],{n,nn}]]] (* _Harvey P. Dale, Nov 18 2013 *)

PARI

t(n)=n*(n+1)/2;
for (n=1,50,c=1; while (c!%t(n)!=0,c++); print1(c","));

Formula

a(n) = A002034(A000217(n)).

Extensions

Extended by Ray Chandler, Jun 06 2008