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A265574 LCM-transform of triangular numbers. 4
1, 3, 2, 5, 1, 7, 2, 3, 1, 11, 1, 13, 1, 1, 2, 17, 1, 19, 1, 1, 1, 23, 1, 5, 1, 3, 1, 29, 1, 31, 2, 1, 1, 1, 1, 37, 1, 1, 1, 41, 1, 43, 1, 1, 1, 47, 1, 7, 1, 1, 1, 53, 1, 1, 1, 1, 1, 59, 1, 61, 1, 1, 2, 1, 1, 67, 1, 1, 1, 71, 1, 73, 1, 1, 1, 1, 1, 79, 1, 3, 1, 83, 1, 1, 1, 1, 1, 89, 1, 1, 1, 1, 1, 1, 1, 97, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
A. Nowicki, Strong divisibility and LCM-sequences, arXiv:1310.2416 [math.NT], 2013.
A. Nowicki, Strong divisibility and LCM-sequences, Am. Math. Mnthly 122 (2015), 958-966.
FORMULA
From Andrey Zabolotskiy, Apr 11 2020: (Start)
a(n) = A051543(n-1) for n>1.
a(n) = A014963(n+1) for n>1. (End)
MAPLE
LCMXfm:=proc(a) local L, i, n, g, b;
L:=nops(a);
g:=Array(1..L, 0); b:=Array(1..L, 0);
b[1]:=a[1]; g[1]:=a[1];
for n from 2 to L do g[n]:=ilcm(g[n-1], a[n]); b[n]:=g[n]/g[n-1]; od;
lprint([seq(b[i], i=1..L)]);
end;
t1:=[seq(n*(n+1)/2, n=1..100)];
LCMXfm(t1);
MATHEMATICA
LCMXfm[a_List] := Module[{L = Length[a], b, g}, b[1] = g[1] = a[[1]]; b[_] = 0; g[_] = 0; Do[g[n] = LCM[g[n - 1], a[[n]]]; b[n] = g[n]/g[n - 1], {n, 2, L}]; Array[b, L]];
LCMXfm[Table[n*(n + 1)/2, {n, 1, 100}]] (* Jean-François Alcover, Dec 05 2017, from Maple *)
CROSSREFS
Sequence in context: A224344 A113260 A051543 * A129538 A076934 A111701
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 02 2016
STATUS
approved

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)