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

Author

David W. Wilson

Keywords

• nonn

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

Crossrefs

Cf. A000040, A002808, A008472.

Programs

Magma

[n:n in [1..300]| IsPrime(&+PrimeDivisors(n)) and not IsPrime(n)]; // Marius A. Burtea, Jan 21 2019

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 *)

PARI

is(n) = isprime(vecsum(factor(n)[, 1])) && !isprime(n) \\ David A. Corneth, Jan 21 2019