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).

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

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

Cf. A002997, A008472.

Sequence in context: A216905 A166383 A227444 * A246250 A126432 A186175

Adjacent sequences: A329460 A329461 A329462 * A329464 A329465 A329466

Keyword

nonn

Author

Amiram Eldar, Nov 13 2019

Status

approved