A141162 Smallest k such that lambda(k) = n, or 0 if there is no such k.

1, 3, 0, 5, 0, 7, 0, 32, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 25, 0, 23, 0, 224, 0, 0, 0, 29, 0, 31, 0, 128, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 115, 0, 47, 0, 119, 0, 0, 0, 53, 0, 81, 0, 928, 0, 59, 0, 61, 0, 0, 0, 256, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 187, 0, 83, 0, 203, 0, 0, 0, 89, 0, 209, 0, 235, 0, 0, 0, 97, 0

Offset: 1

Author

Michel Lagneau, Mar 17 2011

Keywords

• nonn

Comments

Sequence A002174 gives the n such that a(n) > 0. Removing the zeros from this sequence produces A002396. Note that some n appear only for large k. For example, 728 does not appear until k=49184. See A143407 for the largest k that produces a particular value of the lambda function. See A143408 for the number of times each value occurs. - T. D. Noe, Mar 17 2011

Examples

			a(8) = 32 because lambda(32) = 8.
		

Crossrefs

Cf. A002174, A002322 (Carmichael lambda function), A002396, A143407, A143408.

Programs

Maple

with(numtheory):for k from 1 to 100 do:id:=0:for n from 1 to 1000 while(id=0)
  do: if lambda(n) = k then id:=1:printf(`%d, `,n):else fi:od:if id=0 then printf(`%d, `,0):else fi:od:

Mathematica

nn = 100; t = Table[0, {nn}]; Do[c = CarmichaelLambda[k]; If[c <= nn && t[[c]] == 0, t[[c]] = k], {k, 1000}]; t

Formula

a(A002174(n)) = A002396(n).