A227975 Numbers m such that m divides Sum_{k=1..m} lambda(k).

1, 2, 5, 6, 10, 18, 30, 82, 4866, 8784, 10170, 23364, 76296, 247166, 585570, 735480, 848754, 1559520, 2884840, 11272940, 35642420, 56652788, 174935486, 196398413, 679063441, 1398826844, 1542228164, 1665703953, 2699813692, 5734751503

Offset: 1

Author

Michel Lagneau, Jun 17 2016

Keywords

• nonn

Comments

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,...}.

a(31) > 10^10. - Dana Jacobsen, Jul 07 2016

Examples

			5 is in the sequence because 5 divides Sum_{k=1..5} lambda(k) = 1 + 1 + 2 + 2 + 4 = 2*5.
		

Crossrefs

Cf. A002322, A048290, A162578.

Programs

Mathematica

s = 0; Do[s = s + CarmichaelLambda[n]; If[IntegerQ[s/n], Print[n]], {n, 1, 10^9}]

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

Extensions

More terms from Dana Jacobsen, Jul 07 2016