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

1,2

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

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 *)

Prog

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

Crossrefs

Cf. A002034, A011772.

Sequence in context: A371924 A328793 A195782 * A306762 A124938 A198342

Adjacent sequences: A053046 A053047 A053048 * A053050 A053051 A053052

Keyword

easy,nice,nonn

Author

Felice Russo, Feb 25 2000

Status

approved