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A265575
LCM-transform of Euler totient numbers (A000010).
4
1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 5, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 11, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 2, 1, 13, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 41, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,3
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.
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(phi(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[EulerPhi[n], {n, 1, 100}]] (* Jean-François Alcover, Dec 05 2017, from Maple *)
PROG
(PARI)
up_to = 10000;
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); };
v265575 = LCMtransform(vector(up_to, i, eulerphi(i)));
A265575(n) = v265575[n]; \\ Antti Karttunen, Nov 09 2018
CROSSREFS
Cf. A000010.
Other LCM-transforms are A061446, A265574, A265576, A265577, A265578.
Sequence in context: A341621 A074093 A324286 * A352177 A277367 A239936
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 02 2016
STATUS
approved