|
|
A047820
|
|
Composite numbers that become prime after exactly 1 iteration of f(k) = sum of distinct prime factors of k.
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
MATHEMATICA
|
Select[ Range@280, (fi = FactorInteger@#; Plus @@ Last /@ fi > 1 && PrimeQ[Plus @@ First /@ fi]) &] (* Robert G. Wilson v, Dec 09 2005 *)
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|