login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers k >= 1 such that A018804(k) divided by A000010(k) is an integer.
1

%I #33 Oct 01 2022 21:14:44

%S 1,2,4,8,12,16,20,32,36,48,64,100,108,112,128,132,144,192,256,320,324,

%T 432,500,512,576,756,768,784,960,972,1024,1296,1452,1600,1728,1892,

%U 2048,2052,2112,2240,2304,2500,2816,2880,2916,3072,3888,4096,4800,5120,5184,5292,5488

%N Numbers k >= 1 such that A018804(k) divided by A000010(k) is an integer.

%H Paolo Xausa, <a href="/A349725/b349725.txt">Table of n, a(n) for n = 1..1000</a>

%F For n >= 3, a(n) mod 4 = 0. - _Paolo Xausa_, Jul 25 2022

%e A018804(20) = 72, A000010(20) = 8, 72/8 = 9 thus 20 is a term.

%t A018804[n_]:=Apply[Times,Apply[((#1-1)#2/#1+1)#1^#2&,FactorInteger[n],{1}]]; (* After _Amiram Eldar_ in A018804 *)

%t upto=10^5;Join[{1,2},Reap[Do[If[Divisible[A018804[k],EulerPhi[k]],Sow[k]],{k,4,upto,4}]][[-1,-1]]] (* _Paolo Xausa_, Jul 25 2022 *)

%o (PARI) isok(k) = !(sumdiv(k, d, k*eulerphi(d)/d) % eulerphi(k)); \\ _Michel Marcus_, Nov 27 2021

%Y Cf. A000010, A018804.

%K nonn

%O 1,2

%A _Ctibor O. Zizka_, Nov 27 2021