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A076982
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Number of triangular numbers that divide the n-th triangular number.
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8
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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MAPLE
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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);
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MATHEMATICA
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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 *)
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PROG
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(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)]
(PARI) a(n) = sumdiv(n*(n+1)/2, d, ispolygonal(d, 3)); \\ Michel Marcus, Mar 21 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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