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

Author

N. J. A. Sloane, Jan 02 2016

Keywords

• nonn

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.

Crossrefs

Cf. A000010.

Other LCM-transforms are A061446, A265574, A265576, A265577, A265578.

Programs

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 *)

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