A242925 Numbers k such that lambda(k) divides Sum_{j=1..k} lambda(j).

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 15, 16, 18, 19, 20, 24, 30, 31, 34, 40, 42, 44, 60, 72, 80, 83, 130, 132, 136, 195, 208, 218, 232, 254, 258, 259, 260, 264, 272, 276, 305, 306, 408, 420, 440, 464, 504, 560, 585, 586, 594, 595, 609, 624, 636, 715, 819, 840

Offset: 1

Author

Michel Lagneau, May 26 2014

Keywords

• nonn

Comments

Numbers k such that A162578(k)/A002322(k) = Sum_{j=1..k}A002322(j)/ A002322(k) is an integer where lambda(k) is the Carmichael lambda function (A002322).

The corresponding integers are 1, 2, 2, 3, 6, 3, 10, 4, 21, 10, 16, 17, 15, 6, 28, 76, 60, 9, 19, 98, ...

Examples

			12 is in the sequence because A162578(12)/A002322(12) = 42/2 = 21 is an integer.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A194855, A002322, A162578.

Programs

Maple

with(numtheory):nn:=2000:for n from 1 to nn do:p:=lambda(n): s:=sum('lambda(j)', 'j'=1..n):if irem(s,p)=0 then printf(`%d, `,n):else fi:od:

Mathematica

nn = 2000; sums = Accumulate[CarmichaelLambda[Range[nn]]]; Select[Range[nn], Mod[sums[[#]],CarmichaelLambda[#]] == 0 &]