cp's OEIS Frontend

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

%I A076982 #33 Apr 16 2025 05:41:49
%S A076982 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,
%T A076982 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,
%U A076982 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
%N A076982 Number of triangular numbers that divide the n-th triangular number.
%C A076982 Also number of oblong numbers that divide the n-th oblong number.
%C A076982 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
%H A076982 T. D. Noe, <a href="/A076982/b076982.txt">Table of n, a(n) for n = 1..10000</a>
%F A076982 a(n) = A007862(A000217(n)) = A129308(A002378(n)). - _Ray Chandler_, Jun 21 2008
%p A076982 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);
%t A076982 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 *)
%o A076982 (Python)
%o A076982 def aupton(nn):
%o A076982     tri = [i*(i+1)//2 for i in range(1, nn+1)]
%o A076982     return [sum(t%t2 == 0 for t2 in tri[:j+1]) for j, t in enumerate(tri)]
%o A076982 print(aupton(102)) # _Michael S. Branicky_, Dec 10 2021
%o A076982 (PARI) a(n) = sumdiv(n*(n+1)/2, d, ispolygonal(d, 3)); \\ _Michel Marcus_, Mar 21 2023
%Y A076982 Cf. A007862, A000217, A129308, A002378.
%Y A076982 Cf. A000005, A076983, A084260.
%Y A076982 Cf. A137281.
%K A076982 nonn
%O A076982 1,2
%A A076982 _Amarnath Murthy_, Oct 25 2002
%E A076982 More terms from _Lior Manor_, Nov 06 2002
%E A076982 More terms from _Sascha Kurz_, Jan 26 2003