A047820 Composite numbers that become prime after exactly 1 iteration of f(k) = sum of distinct prime factors of k.

4, 6, 8, 9, 10, 12, 16, 18, 20, 22, 24, 25, 27, 32, 34, 36, 40, 44, 48, 49, 50, 54, 58, 64, 68, 72, 80, 81, 82, 88, 96, 100, 108, 116, 118, 121, 125, 128, 136, 142, 144, 160, 162, 164, 165, 169, 176, 192, 200, 202, 210, 214, 216, 232, 236, 242, 243, 250, 256, 272

Offset

1,1

Comments

f(k) = sum of prime factors without multiplicity, so that f(1500) = 2+3+5 = 10.

The sequence is infinite because f(2^m * 5^s) = 2 + 5 = 7, for m,s >= 1. - Marius A. Burtea, Jan 21 2019

Links

Marius A. Burtea, Table of n, a(n) for n = 1..10122

Mathematica

Select[ Range@280, (fi = FactorInteger@#; Plus @@ Last /@ fi > 1 && PrimeQ[Plus @@ First /@ fi]) &] (* Robert G. Wilson v, Dec 09 2005 *)
Select[Range[300], CompositeQ[#]&&PrimeQ[Total[FactorInteger[#][[;; , 1]]]]&] (* Harvey P. Dale, Sep 18 2024 *)

Prog

(Magma) [n:n in [1..300]| IsPrime(&+PrimeDivisors(n)) and not IsPrime(n)]; // Marius A. Burtea, Jan 21 2019
(PARI) is(n) = isprime(vecsum(factor(n)[, 1])) && !isprime(n) \\ David A. Corneth, Jan 21 2019

Crossrefs

Cf. A000040, A002808, A008472.

Sequence in context: A141607 A071070 A275722 * A248807 A034878 A173328

Adjacent sequences: A047817 A047818 A047819 * A047821 A047822 A047823

Keyword

nonn

Author

David W. Wilson

Status

approved