A199013 Numbers which, when divided by the sum of their prime factors, give a prime number.

16, 27, 30, 60, 70, 105, 220, 231, 286, 476, 627, 646, 805, 897, 1160, 1276, 1581, 1776, 1798, 2322, 2408, 2967, 3055, 3196, 3526, 4028, 4543, 5360, 5487, 6248, 6461, 6745, 7198, 7881, 7968, 9628, 9717, 10366, 10707, 10864, 11036, 14231, 15368, 15836, 16377, 19304

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

Subsequence of A046346.

Sequence in context: A043126 A043906 A152444 * A374007 A118642 A088247

Adjacent sequences: A199010 A199011 A199012 * A199014 A199015 A199016

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