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

%I A306762 #17 Mar 11 2019 20:15:55
%S A306762 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,
%T A306762 17,55,10,58,15,71,16,44,19,169,24,100,11,48,12,25,49,18,26,38,30,40,
%U A306762 23,164,28,50,13,141,20,47,55,21,14,80,58,192,15,110,71,76
%N A306762 Smallest integer k such that Sum_(i=1..k) lambda(i) is divisible by n, where lambda(i) is the Carmichael lambda function.
%e A306762 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.
%p A306762 S:= ListTools:-PartialSums(map(numtheory:-lambda, [$1..500])):
%p A306762 N:= 100: count:= 0: V:= Vector(N):
%p A306762 for n from 1 to 500 while count < N do
%p A306762    d:= select(t -> t <= N and V[t] = 0, numtheory:-divisors(S[n]));
%p A306762    count:= count + nops(d);
%p A306762    V[convert(d,list)]:= n;
%p A306762 od:
%p A306762 convert(V,list); # _Robert Israel_, Mar 11 2019
%t A306762 a[n_] := (m = 1; While[! IntegerQ[Sum[CarmichaelLambda[k], {k, 1, m}]/n], m++]; m); a /@ Range[80]
%o A306762 (PARI) lambda(n) = lcm(znstar(n)[2]);
%o A306762 a(n) = {my(k=1, s=lambda(k)); while (s % n, k++; s += lambda(k)); k;} \\ _Michel Marcus_, Mar 09 2019
%Y A306762 Cf. A002322 (Carmichael lambda), A162578 (partial sums of A002322).
%Y A306762 Cf. A053049 (analog with totient function).
%K A306762 nonn,easy
%O A306762 1,2
%A A306762 _Michel Lagneau_, Mar 08 2019