A053049 - OEIS

%I #17 Aug 03 2021 15:08:29

%S 1,2,4,3,5,4,9,10,7,5,8,6,46,9,19,10,18,7,60,16,11,8,12,15,22,46,29,9,

%T 13,19,51,10,36,18,21,15,88,60,142,16,67,11,23,31,24,12,55,17,40,22,

%U 18,153,26,29,184,75,84,13,92,19

%N Smallest integer m such that sum_(k=1 to m) phi(k) is divisible by n, where phi(k) is the totient function.

%D Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000

%H T. D. Noe, <a href="/A053049/b053049.txt">Table of n, a(n) for n = 1..1000</a>

%t a[n_] := (m = 1; While[! IntegerQ[Sum[EulerPhi[k], {k, 1, m}]/n], m++]; m); a /@ Range[60] (* _Jean-François Alcover_, Jul 20 2011 *)

%t Module[{nn=60,ep=Accumulate[EulerPhi[Range[200]]]},Table[Position[ep,_?(Divisible[ #,n]&),1,1],{n,nn}]]//Flatten (* _Harvey P. Dale_, Aug 03 2021 *)

%o (PARI) a(n)=my(m=1,s=Mod(1,n));while(s,s+=eulerphi(m++));m \\ _Charles R Greathouse IV_, Feb 24 2012

%Y Cf. A002034, A011772.

%K easy,nice,nonn

%O 1,2

%A _Felice Russo_, Feb 25 2000