cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A241475 Triangle t(n,r) = s(n,r)*s(n,r+1), where s(n,r) = lcm(n,n-1,...,n-r+1)/lcm(1,2,...,r-1,r), n >= 1 and 0 <= r < n.

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%I A241475 #15 Mar 04 2018 09:38:53
%S A241475 1,2,2,3,9,3,4,24,12,2,5,50,100,50,5,6,90,150,50,5,1,7,147,735,1225,
%T A241475 245,49,7,8,224,784,1960,980,196,28,2,9,324,3024,3528,1764,1764,252,
%U A241475 18,3,10,450,2700,12600,8820,1764,252,18,3,1,11,605,9075,54450,152460,213444,30492,2178,363,121,11
%N A241475 Triangle t(n,r) = s(n,r)*s(n,r+1), where s(n,r) = lcm(n,n-1,...,n-r+1)/lcm(1,2,...,r-1,r), n >= 1 and 0 <= r < n.
%C A241475 The first eight terms and the first two terms of every row are identical to those of A132812.
%H A241475 S. M. Khairnar, Anant W. Vyawahare and J. N. Salunkhe, <a href="http://vixra.org/pdf/1403.0253v1.pdf">On Smarandache least common multiple ratio</a>, Scientia Magna Vol. 5 (2009), No. 1, 29-36.
%H A241475 Amarnath Murthy, <a href="http://vixra.org/pdf/1403.0911v1.pdf">Some Notions on Least Common Multiples</a>, Smarandache Notions Journal, Vol. 12, No. 1-2-3, Spring 2001.
%e A241475 Triangle begins:
%e A241475   1;
%e A241475   2,  2;
%e A241475   3,  9,   3;
%e A241475   4, 24,  12,  2;
%e A241475   5, 50, 100, 50, 5;
%e A241475   6, 90, 150, 50, 5, 1;
%e A241475   ...
%t A241475 s[_, 0] = 1; s[n_, r_?NumericQ] := LCM @@ Table[n-k+1, {k, 1, r}] / LCM @@ Table[k, {k, 1, r}]; t[n_, r_] := s[n, r]*s[n, r+1]; Table[t[n, r] , {n, 1, 12}, {r, 0, n-1}] // Flatten
%Y A241475 Cf. A067049, A093430, A132812.
%K A241475 nonn,tabl
%O A241475 1,2
%A A241475 _Jean-François Alcover_, Apr 23 2014