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A199013
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Numbers which, when divided by the sum of their prime factors, give a prime number.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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220/(2+2+5+11)=220/20=11, which is prime, so 220 is in the sequence.
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MATHEMATICA
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dspfQ[n_]:=Module[{c=Total[Flatten[Table[#[[1]], {#[[2]]}]&/@FactorInteger[ n]]]}, PrimeQ[n/c]]; Select[Range[20000], dspfQ] (* Harvey P. Dale, Mar 19 2013 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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