OFFSET
1,1
COMMENTS
One of the prime factors of n disappears in the sum of its prime factors’ prime factors. The sequence includes 2p(p+2) whenever p and p+2 are twin primes. There are no primes or semiprimes in the sequence.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
EXAMPLE
220/(2+2+5+11)=220/20=11, which is prime, so 220 is in the sequence.
MATHEMATICA
dspfQ[n_]:=Module[{c=Total[Flatten[Table[#[[1]], {#[[2]]}]&/@FactorInteger[ n]]]}, PrimeQ[n/c]]; Select[Range[20000], dspfQ] (* Harvey P. Dale, Mar 19 2013 *)
PROG
(PARI) is(n)=my(f=factor(n), t); for(i=1, #f[, 1], t+=f[i, 1]*f[i, 2]); if(t&&n%t, 0, isprime(n/t)) \\ Charles R Greathouse IV, Nov 06 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Nico Brown, Nov 06 2011
EXTENSIONS
a(22) corrected, a(30)-a(46) from Charles R Greathouse IV, Nov 06 2011
STATUS
approved