A306762 Smallest integer k such that Sum_(i=1..k) lambda(i) is divisible by n, where lambda(i) is the Carmichael lambda function.

1, 2, 4, 3, 5, 4, 12, 11, 7, 5, 49, 6, 9, 12, 10, 15, 16, 7, 24, 8, 12, 49, 26, 30, 23, 9, 13, 17, 55, 10, 58, 15, 71, 16, 44, 19, 169, 24, 100, 11, 48, 12, 25, 49, 18, 26, 38, 30, 40, 23, 164, 28, 50, 13, 141, 20, 47, 55, 21, 14, 80, 58, 192, 15, 110, 71, 76

Offset

1,2

Links

Table of n, a(n) for n=1..67.

Example

a(7) = 12 because Sum_{i=1..12} lambda(i) = 1 + 1 + 2 + 2 + 4 + 2 + 6 + 2 + 6 + 4 + 10 + 2 = 42, and 42/7 = 6.

Maple

S:= ListTools:-PartialSums(map(numtheory:-lambda, [$1..500])):
N:= 100: count:= 0: V:= Vector(N):
for n from 1 to 500 while count < N do
   d:= select(t -> t <= N and V[t] = 0, numtheory:-divisors(S[n]));
   count:= count + nops(d);
   V[convert(d, list)]:= n;
od:
convert(V, list); # Robert Israel, Mar 11 2019

Mathematica

a[n_] := (m = 1; While[! IntegerQ[Sum[CarmichaelLambda[k], {k, 1, m}]/n], m++]; m); a /@ Range[80]

Prog

(PARI) lambda(n) = lcm(znstar(n)[2]);
a(n) = {my(k=1, s=lambda(k)); while (s % n, k++; s += lambda(k)); k; } \\ Michel Marcus, Mar 09 2019

Crossrefs

Cf. A002322 (Carmichael lambda), A162578 (partial sums of A002322).

Cf. A053049 (analog with totient function).

Sequence in context: A328793 A195782 A053049 * A124938 A198342 A081725

Adjacent sequences: A306759 A306760 A306761 * A306763 A306764 A306765

Keyword

nonn,easy

Author

Michel Lagneau, Mar 08 2019

Status

approved