OFFSET
1,1
COMMENTS
Subsequence of the Carmichael numbers (A002997).
Composite numbers k such that (k-1) == lambda(k) (mod phi(k)).
Problem: are there infinitely many such numbers?
Conjecture: these are numbers k such that phi(k) + lambda(k) = k - 1. Checked up to 2^64. - Amiram Eldar and Thomas Ordowski, Dec 06 2019
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..239 (terms below 10^22 calculated using data from Claude Goutier; terms 1..79 from Robert Israel)
MAPLE
# Using data files for A002997
count:= 0:
for cfile in ["carmichael-16", "carmichael17", "carmichael18"] do
do
S:= readline(cfile);
if S = 0 then break fi;
L:= map(parse, StringTools:-Split(S));
n:= L[1]; pm:= map(`-`, L[2..-1], 1);
phin:= convert(pm, `*`);
lambdan:= ilcm(op(pm));
if n-1 - lambdan mod phin = 0 then
count:= count+1; A[count]:= n;
fi
od:
fclose(cfile);
od:
seq(A[i], i=1..count); # Robert Israel, Jul 26 2017
MATHEMATICA
Select[Range[10^8], Divisible[# - 1, (lam = CarmichaelLambda[#])] && Mod[# - 1, EulerPhi[#]] == lam &] (* Amiram Eldar, Dec 06 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel and Thomas Ordowski, Jul 25 2017
STATUS
approved