A053049 Smallest integer m such that sum_(k=1 to m) phi(k) is divisible by n, where phi(k) is the totient function.

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, 13, 19, 51, 10, 36, 18, 21, 15, 88, 60, 142, 16, 67, 11, 23, 31, 24, 12, 55, 17, 40, 22, 18, 153, 26, 29, 184, 75, 84, 13, 92, 19

Offset: 1

Author

Felice Russo, Feb 25 2000

Keywords

• easy
• nice
• nonn

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002034, A011772.

Programs

Mathematica

a[n_] := (m = 1; While[! IntegerQ[Sum[EulerPhi[k], {k, 1, m}]/n], m++]; m); a /@ Range[60] (* Jean-François Alcover, Jul 20 2011 *)
Module[{nn=60,ep=Accumulate[EulerPhi[Range[200]]]},Table[Position[ep,?(Divisible[ #,n]&),1,1],{n,nn}]]//Flatten (* _Harvey P. Dale, Aug 03 2021 *)

PARI

a(n)=my(m=1,s=Mod(1,n));while(s,s+=eulerphi(m++));m \\ Charles R Greathouse IV, Feb 24 2012