OFFSET
1,2
COMMENTS
Terms of A002322, sorted and multiple values taken just once. - Vladimir Joseph Stephan Orlovsky, Jul 21 2009
a(2445343) = 10^7, suggesting that Luca & Pomerance's lower bound may be closer to the truth than the upper bound. The fit exponent log a(n)/log n - 1 = 0.0957... in this case. - Charles R Greathouse IV, Jul 02 2017
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
D. H. Lehmer, Guide to Tables in the Theory of Numbers, Bulletin No. 105, National Research Council, Washington, DC, 1941, pp. 7-10.
Florian Luca and Carl Pomerance, On the range of Carmichael's universal-exponent function, Acta Arithmetica 162 (2014), pp.289-308.
C. Moreau, Sur quelques théorèmes d'arithmétique, Nouvelles Annales de Mathématiques, 17 (1898), 293-307.
FORMULA
n (log n)^0.086 << a(n) << n (log n)^0.36 where << is the Vinogradov symbol, see Luca & Pomerance. - Charles R Greathouse IV, Dec 28 2013
MATHEMATICA
lst={}; Do[AppendTo[lst, CarmichaelLambda[n]], {n, 6*7!}]; lst; Take[Union[lst], 123] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2009 *)
(* warning: there seems to be no guarantee that no terms near the end are omitted! - Joerg Arndt, Dec 23 2014 *)
TakeWhile[Union@ Table[CarmichaelLambda@ n, {n, 10^6}], # <= 168 &] (* Michael De Vlieger, Mar 19 2016 *)
PROG
(PARI) list(lim)=my(v=List([1]), u, t); forprime(p=3, lim\3+1, u=List(); listput(u, p-1); while((t=u[#u]*p)<=lim, listput(u, t)); for(j=1, #v, for(i=1, #u, t=lcm(u[i], v[j]); if(t<=lim && t!=v[j], listput(v, t)))); v=List(Set(v))); forprime(p=lim\3+2, lim+1, listput(v, p-1)); v=List(Set(v)); for(i=1, #v, t=2*v[i]; if(t>lim, break); listput(v, t); while((t*=2)<=lim, listput(v, t))); Set(v) \\ Charles R Greathouse IV, Jun 23 2017
(PARI) is(n)=if(n%2, return(n==1)); my(f=factor(n), pe); for(i=1, #f~, if(n%(f[i, 1]-1)==0, next); pe=f[i, 1]^f[i, 2]; forstep(q=2*pe+1, n+1, 2*pe, if(n%(q-1)==0 && isprime(q), next(2))); return(0)); 1 \\ Charles R Greathouse IV, Jun 25 2017
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from T. D. Noe, Aug 13 2008
STATUS
approved