login
a(n) = max(core(n),phi(n)) where core(n) is the squarefree part of n.
2

%I #11 Sep 03 2020 06:42:09

%S 1,2,3,2,5,6,7,4,6,10,11,4,13,14,15,8,17,6,19,8,21,22,23,8,20,26,18,

%T 12,29,30,31,16,33,34,35,12,37,38,39,16,41,42,43,20,24,46,47,16,42,20,

%U 51,24,53,18,55,24,57,58,59,16,61,62,36,32,65,66,67,32,69,70,71,24,73,74

%N a(n) = max(core(n),phi(n)) where core(n) is the squarefree part of n.

%H Amiram Eldar, <a href="/A076685/b076685.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{k=1..n} a(k) is asymptotic to c*n^2 with c = 0.3938......

%t core[n_] := Times @@ (First[#]^Mod[Last[#], 2]& /@ FactorInteger[n]); a[n_] := Max[EulerPhi[n], core[n]]; Array[a, 80] (* _Amiram Eldar_, Sep 03 2020 *)

%o (PARI) a(n)=if(n<1,0,max(core(n),eulerphi(n)))

%Y Cf. A000010, A007913, A076686.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Oct 25 2002