OFFSET
1,1
COMMENTS
A309132(m) divides m for all Carmichael numbers m, but apparently most of them equal A309132(m). Of the first 10000 Carmichael numbers, only 1341 are in this sequence.
The ratios a(n)/A309132(a(n)) are 3, 5, 13, 7, 133, 7, 133, 7, 7, 793, 7, 13, 13, ...
By Jonathan Sondow's theorem (cf. comments in A309132), these are Carmichael numbers m such that denominator(Sum_{prime p|m}1/p - 1/m) < m, i.e., A326690(m) < m.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
aQ[n_] := CompositeQ[n] && Divisible[n - 1, CarmichaelLambda[n]] && Denominator[ Total@(1/FactorInteger[n][[;; , 1]]) - 1/n] < n; Select[Range[10^6], aQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar and Thomas Ordowski, Jul 20 2019
STATUS
approved