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%I #45 Jul 08 2016 06:34:39
%S 1,2,5,6,10,18,30,82,4866,8784,10170,23364,76296,247166,585570,735480,
%T 848754,1559520,2884840,11272940,35642420,56652788,174935486,
%U 196398413,679063441,1398826844,1542228164,1665703953,2699813692,5734751503
%N Numbers m such that m divides Sum_{k=1..m} lambda(k).
%C lambda(n) is the Carmichael lambda function (A002322). The corresponding ratios (Sum_{k=1..m} lambda(k))/m are given by the sequence {1, 1, 2, 2, 3, 5, 8, 19, 711, 1221, 1399, 3011, 9034, 27187, 61246, 75971, 86971, 154710, 277344, 1015576,...}.
%C a(31) > 10^10. - _Dana Jacobsen_, Jul 07 2016
%e 5 is in the sequence because 5 divides Sum_{k=1..5} lambda(k) = 1 + 1 + 2 + 2 + 4 = 2*5.
%t s = 0; Do[s = s + CarmichaelLambda[n]; If[IntegerQ[s/n], Print[n]], {n, 1, 10^9}]
%o (Perl) use ntheory ":all"; my $v=0; for my $m (1..1e6) { $v=vecsum($v,carmichael_lambda($m)); say $m unless $v % $m; } # _Dana Jacobsen_, Jul 07 2016
%Y Cf. A002322, A048290, A162578.
%K nonn
%O 1,2
%A _Michel Lagneau_, Jun 17 2016
%E More terms from _Dana Jacobsen_, Jul 07 2016