OFFSET
1,3
COMMENTS
lambda(n) is the Carmichael lambda function A002322.
a(n) = 0 for n = 209, 297, 413, 418, 517, ...
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 A143417 (see the b-file in A143417). For example:
a(n) = 3 for n = 3, 4, 6;
a(n) = 5 for n = 5, 10, 15, 16, 20, 30, 40, 48, 60, 80, 120, 240;
a(n) = 7 for n = 7, 9, 14, 18, 21, 28, ..., 480;
a(n) = 11 for n = 11, 22, 33, 44, 66, 88, 132, 264;
a(n) = 13 for n = 13, 26, 35, 39, ..., 65520.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
EXAMPLE
a(6) = 3 because phi(3) = lambda(6) = 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(k)=lambda(n) 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[k]==CarmichaelLambda[n], k++]; k, {n, 100}]
Join[{1}, Module[{nn=100, ep, lam}, ep=Table[{k, EulerPhi[k]}, {k, nn}]; Table[ SelectFirst[ep, #[[2]]==CarmichaelLambda[n]&], {n, 2, nn}]][[All, 1]]] (* Harvey P. Dale, Dec 24 2021 *)
PROG
(PARI) a(n)=my(t=lcm(znstar(n)[2])); if(t>2, for(k=t+1, solve(x=t, 2*t^2, x/(exp(Euler)*log(log(x))+3/log(log(x)))-t), if(eulerphi(k)==t, return(k))); 0, 2*t-1) \\ Charles R Greathouse IV, Nov 28 2012
(PARI)
A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))} \\ This function from M. F. Hasler, Oct 05 2009
A219792(n) = { my(x=lcm(znstar(n)[2])); if(0==A014197(x), 0, for(k=1, oo, if(eulerphi(k)==x, return(k)))); }; \\ Antti Karttunen, Dec 05 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 28 2012
STATUS
approved