login
A329463
Carmichael numbers k such that sopf(k) is also a Carmichael number, where sopf(k) is the sum of the distinct primes dividing k (A008472).
1
1618206745, 2265650401, 28645206001, 56969031001, 226244724265, 235389006721, 235771174081, 296423001601, 432133594201, 626086650961, 772165132201, 884500464001, 1167647270401, 4384350028801, 4714081284241, 5438971500481, 5916902791801, 7160462614273, 11458124974801
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
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
Sequence in context: A216905 A166383 A227444 * A246250 A373001 A126432
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 13 2019
STATUS
approved