login
A290281
Numbers k such that (k-1) mod phi(k) = lambda(k), where phi = A000010 and lambda = A002322.
1
6601, 11972017, 34657141, 67902031, 139952671, 258634741, 2000436751, 8801128801, 9116583841, 9462932431, 38069223721, 326170416001, 359316634951, 1860929324101, 2022188518351, 2283475947391, 2648686458601, 2697891108151, 4513362899761, 5020030521001, 5472940991761, 6163867710001, 7507903975951, 19288340548471
OFFSET
1,1
COMMENTS
Numbers k such that A215486(k) = A002322(k).
Subsequence of the Carmichael numbers (A002997).
Composite numbers k such that (k-1) == lambda(k) (mod phi(k)).
Composite numbers k such that A277127(k) == 1 (mod A000010(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
Subsequence of A264012.
Sequence in context: A164971 A214434 A317247 * A178213 A237320 A237726
KEYWORD
nonn
AUTHOR
STATUS
approved