

A219793


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


1



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
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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



