OFFSET
1,2
COMMENTS
Terms larger than one occur at n = 2, 4, 6, 16, 24, 36, 64, 120, 840, 900, 1296, 7560, 44100, 46656, 83160, ... - Antti Karttunen, Nov 06 2018
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
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.
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
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;
with(numtheory);
t1:=[seq(tau(n), 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[DivisorSigma[0, n], {n, 1, 100}]] (* Jean-François Alcover, Dec 05 2017, from Maple *)
PROG
(PARI)
up_to = 16384;
LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2, len, g[n] = lcm(g[n-1], v[n]); b[n] = g[n]/g[n-1]); (b); };
v265578 = LCMtransform(vector(up_to, i, numdiv(i)));
A265578(n) = v265578[n]; \\ Antti Karttunen, Nov 06 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 02 2016
STATUS
approved