Select[Range[2000], MemberQ[FoldList[Plus, 0, Divisors[#]], CarmichaelLambda[#]] &] (* _T. D. Noe, _, Aug 29 2011 *)

_Michel Lagneau (mn.lagneau2(AT)orange.fr), _, Aug 28 2011

editing

approved

LambdaNumbers n such that lambda(n) is the sum of the first k divisors of n for some k.

Cf. A072278, A002322, A072278.

a = {}; For[j = 1, j <= 2000, j++, s = 0; d = Divisors[j]; l = Length[d]; e = CarmichaelLambda[j]; For[i = 1, i <= l, i++, s = s + d[[i]]; If[s == e, a = Append[a, j]; Break]]]; a

Select[Range[2000], MemberQ[FoldList[Plus, 0, Divisors[#]], CarmichaelLambda[#]] &] (* T. D. Noe, Aug 29 2011 *)

Lambda(n) is the Carmichael lambda function (A002322).

The divisors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140 and lambda(140) = 12 = 1 + 2 + 4 + 5; hence 140 belongs to the sequence.

Cf. A072278 , A002322.

proposed

editing

editing

proposed

The divisors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140 and lambda(140) = 12 = 1 + 2 + 4 + 5; hence 140 belongs to the sequence.

proposed

editing

editing

proposed

allocated Lambda(n) is the sum of the first k divisors of n for Michel Lagneausome k.

1, 2, 15, 18, 36, 42, 72, 78, 84, 126, 132, 140, 165, 168, 192, 200, 204, 234, 252, 260, 264, 270, 280, 288, 348, 400, 408, 440, 462, 504, 520, 546, 560, 741, 816, 825, 880, 882, 888, 912, 1040, 1044, 1248, 1464, 1470, 1632, 1638, 1692, 1710, 1749

1,2

Lambda(n) is the Carmichael lambda function (A002322).

with(numtheory):for n from 1 to 2500 do:x:=divisors(n):n1:=nops(x):s:=0:for k from 1 to n1 while(s<=n) do:s:=s+x[k]:if s= lambda(n) then printf(`%d, `, n):else fi:od:od:

a = {}; For[j = 1, j <= 2000, j++, s = 0; d = Divisors[j]; l = Length[d]; e = CarmichaelLambda[j]; For[i = 1, i <= l, i++, s = s + d[[i]]; If[s == e, a = Append[a, j]; Break]]]; a

Cf. A072278 A002322.

allocated

nonn

Michel Lagneau (mn.lagneau2(AT)orange.fr), Aug 28 2011

approved

editing