A076982 Number of triangular numbers that divide the n-th triangular number.

1, 2, 3, 2, 3, 3, 2, 4, 4, 2, 4, 4, 2, 5, 6, 2, 3, 3, 3, 8, 4, 2, 4, 6, 2, 3, 5, 2, 4, 4, 2, 5, 3, 2, 10, 4, 2, 3, 7, 3, 4, 4, 2, 9, 5, 2, 4, 6, 2, 4, 5, 2, 3, 6, 5, 6, 3, 2, 6, 6, 2, 4, 7, 3, 5, 3, 2, 4, 6, 2, 5, 5, 2, 4, 7, 2, 6, 3, 3, 9, 3, 2, 5, 10, 2, 3, 5, 2, 5, 8, 3, 4, 3, 2, 8, 4, 2, 5, 10, 3, 3, 3

Offset: 1

Author

Amarnath Murthy, Oct 25 2002

Keywords

• nonn

Comments

Also number of oblong numbers that divide the n-th oblong number.

Sequence A137281 contains the indices of primitive triangular numbers; those that have no triangular divisors other than 1 and itself. - T. D. Noe, Apr 12 2011

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007862, A000217, A129308, A002378.

Cf. A000005, A076983, A084260.

Cf. A137281.

Programs

Maple

a[1] := 1:for i from 1 to 200 do s := 0:for j from 1 to i do if((i*(i+1)/2 mod j*(j+1)/2)=0) then s := s+1:fi:od:a[i] := s:od:seq(a[l],l=1..200);

Mathematica

nn = 100; tri = Table[n*(n+1)/2, {n, nn}]; Table[Count[Mod[tri[[n]], Take[tri, n]], 0], {n, nn}] (* T. D. Noe, Apr 12 2011 *)

PARI

a(n) = sumdiv(n*(n+1)/2, d, ispolygonal(d, 3)); \\ Michel Marcus, Mar 21 2023

Python

def aupton(nn):
    tri = [i*(i+1)//2 for i in range(1, nn+1)]
    return [sum(t%t2 == 0 for t2 in tri[:j+1]) for j, t in enumerate(tri)]
print(aupton(102)) # Michael S. Branicky, Dec 10 2021

Formula

a(n) = A007862(A000217(n)) = A129308(A002378(n)). - Ray Chandler, Jun 21 2008

Extensions

More terms from Lior Manor, Nov 06 2002

More terms from Sascha Kurz, Jan 26 2003