A069752 Smallest k>n such that the triangular number n*(n+1)/2 divides the triangular number k*(k+1)/2.

2, 3, 8, 15, 9, 14, 48, 63, 35, 44, 32, 39, 77, 20, 80, 255, 135, 152, 75, 35, 77, 230, 183, 200, 299, 324, 188, 203, 144, 155, 960, 351, 153, 84, 224, 296, 665, 246, 104, 615, 245, 258, 472, 99, 414, 1034, 704, 735, 1175, 374, 272, 636, 1377, 539, 175, 399, 551

Offset: 1

Author

Benoit Cloitre, May 01 2002

Keywords

• easy
• nonn

Comments

Note that k <= n^2-1, with equality occurring only if n and n+1 are a prime and a power of 2 (in either order); that is, when n is a Mersenne prime or n+1 is a Fermat prime. - T. D. Noe, Apr 08 2011

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A068084, A188621.

Programs

Mathematica

Clear[k]; Join[{2}, Table[Reduce[k*(k+1) == 0, k, Modulus -> n*(n+1)][[3, 2]], {n, 2, 100}]] (* T. D. Noe, Apr 08 2011 *)

PARI

for(s=1,1000,s1=s*(s+1);n=s+1; while(n*(n+1)%s1>0,n++); print1(n,","); ) \\ Zak Seidov, Apr 08 2011