A219793 Least k such that phi(n) = lambda(k), or 0 if there is no such k.

1, 1, 3, 3, 5, 3, 7, 5, 7, 5, 11, 5, 13, 7, 32, 32, 17, 7, 19, 32, 13, 11, 23, 32, 25, 13, 19, 13, 29, 32, 31, 17, 25, 17, 224, 13, 37, 19, 224, 17, 41, 13, 43, 25, 224, 23, 47, 17, 43, 25, 128, 224, 53, 19, 41, 224, 37, 29, 59, 17, 61, 31, 37, 128, 119, 25

Offset

1,3

Comments

lambda(n) is the Carmichael lambda function A002322. For n <10000, it appears that a(n) = 0 for n = 2047, 4094, 6141, 6533, 8119, 8188, 9637. if a(n) = p is a prime greater than 2, then n belongs to the finite set {p, p1, p2, ...., pk} that is a subsequence of A032447 (see the array with characteristic rows in the example of A032447), for example : a(n) = 3 for n = 3, 4, 6; a(n) = 5 for n = 5, 8, 10, 12; a(n) = 7 for n = 7, 9, 14, 18, 15, 16, 20, 24, 30; a(n) = 11 for n = 11, 22; a(n) = 13 for n = 13, 21, 26, 28, 36, 42; a(n) = 17 for n = 17, 32, 34, 40, 48, 60.

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

a(6) = 3 because phi(6) = lambda(3) = 2.

Maple

with(numtheory): for n from 1 to 100 do: ii:=0:for k from 1 to 10^6 while(ii=0) do:if phi(n)=lambda(k) then ii:=1: printf(`%d, `, k):else fi:od:if ii=0 then printf(`%d, `, 0): else fi:od:

Mathematica

Table[k=0; While[!EulerPhi[n] == CarmichaelLambda[k], k++]; k, {n, 100}] (* program will go into an infinite loop at n = 2047 *)

Crossrefs

Cf. A002322, A032447, A141162, A143407.

Sequence in context: A219792 A029622 A015126 * A215495 A335115 A299149

Adjacent sequences: A219790 A219791 A219792 * A219794 A219795 A219796

Keyword

nonn

Author

Michel Lagneau, Nov 28 2012

Status

approved