cp's OEIS Frontend

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

%I A265575 #19 Nov 09 2018 21:59:09
%S A265575 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,
%T A265575 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,
%U A265575 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
%N A265575 LCM-transform of Euler totient numbers (A000010).
%H A265575 Antti Karttunen, <a href="/A265575/b265575.txt">Table of n, a(n) for n = 1..26003</a>
%H A265575 Antti Karttunen, <a href="/A265575/a265575.txt">Data supplement: n, a(n) computed for n =  1..100000</a>
%H A265575 A. Nowicki, <a href="http://arxiv.org/abs/1310.2416">Strong divisibility and LCM-sequences</a>, arXiv:1310.2416 [math.NT], 2013.
%H A265575 A. Nowicki, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.122.10.958">Strong divisibility and LCM-sequences</a>, Am. Math. Mnthly 122 (2015), 958-966.
%p A265575 LCMXfm:=proc(a) local L,i,n,g,b;
%p A265575 L:=nops(a);
%p A265575 g:=Array(1..L,0); b:=Array(1..L,0);
%p A265575 b[1]:=a[1]; g[1]:=a[1];
%p A265575 for n from 2 to L do g[n]:=ilcm(g[n-1],a[n]); b[n]:=g[n]/g[n-1]; od;
%p A265575 lprint([seq(b[i],i=1..L)]);
%p A265575 end;
%p A265575 with(numtheory);
%p A265575 t1:=[seq(phi(n),n=1..100)];
%p A265575 LCMXfm(t1);
%t A265575 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]];
%t A265575 LCMXfm[Table[EulerPhi[n], {n, 1, 100}]] (* _Jean-François Alcover_, Dec 05 2017, from Maple *)
%o A265575 (PARI)
%o A265575 up_to = 10000;
%o A265575 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); };
%o A265575 v265575 = LCMtransform(vector(up_to,i,eulerphi(i)));
%o A265575 A265575(n) = v265575[n]; \\ _Antti Karttunen_, Nov 09 2018
%Y A265575 Cf. A000010.
%Y A265575 Other LCM-transforms are A061446, A265574, A265576, A265577, A265578.
%K A265575 nonn
%O A265575 1,3
%A A265575 _N. J. A. Sloane_, Jan 02 2016