OFFSET
1,1
COMMENTS
There are 1108 terms below 2^64: 75 have 5 prime factors, 1 have 7 prime factors (307696492063107001), and 1032 have 9 prime factors.
The corresponding values of sopf(a(n)) are 1729, 1105, 1105, 1105, 115921, 2821, 2821, 2821, 15841, 2821, 1729, 10585, 2821, 2821, 75361, 2821, 15841, 2821, 334153, ...
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1108
EXAMPLE
1618206745 = 5 * 23 * 43 * 229 * 1429 is a Carmichael number, and 5 + 23 + 43 + 229 + 1429 = 1729 is also a Carmichael number.
MATHEMATICA
carmQ[n_] := CompositeQ[n] && Divisible[n - 1, CarmichaelLambda[n]]; sopf[n_] := Total[FactorInteger[n][[;; , 1]]]; s={}; Do[If[carmQ[n] && carmQ[sopf[n]], AppendTo[s, n]], {n, 2, 3*10^10}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 13 2019
STATUS
approved