A265575 LCM-transform of Euler totient numbers (A000010).

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

Antti Karttunen, Table of n, a(n) for n = 1..26003

Antti Karttunen, Data supplement: n, a(n) computed for n =  1..100000

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

Adjacent sequences: A265572 A265573 A265574 * A265576 A265577 A265578

Keyword

nonn

Author

N. J. A. Sloane, Jan 02 2016

Status

approved