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 A193458 Union of A071863 and A071861. 0
 5, 44, 51, 54, 90, 328, 390, 423, 608, 1679, 1805, 1825, 2000, 2294, 2448, 2755, 2847, 3008, 3103, 3145, 3289, 3354, 3509, 3737, 3887, 4929, 5695, 6024, 6344, 7080, 8509, 8949, 9085, 9379, 9453, 9675, 9685, 10286, 10584, 10730, 10787, 10933, 11725, 12035, 12193, 12462, 12499, 12564 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers n such that the sum of primes dividing n (with multiplicity, as in A001414) is a prime factor of n+1, or such that the sum of primes of n+1 is a prime factor of n. LINKS EXAMPLE For n = 54 = 2*3*3*3 we have sopfr(54) = 2 + 3 + 3 + 3 = 11 and n+1 = 55 = 5*11 has a prime factor 11 = sopfr(54). Therefore n=54 is in the sequence. MAPLE A001414 := proc(n) add( op(1, d)*op(2, d), d = ifactors(n)[2]) ; end proc: isA071863 := proc(n) spf := A001414(n) ; for p in numtheory[factorset](n+1) do if p = spf then return true; end if; end do: false; end proc: isA071861 := proc(n) spf := A001414(n+1) ; for p in numtheory[factorset](n) do if p = spf then return true; end if; end do: false; end proc: isA193458 := proc(n) isA071863(n) or isA071861(n) ; end proc: for n from 2 to 20000 do if isA193458(n) then printf("%d, ", n); end if; end do: # R. J. Mathar, Aug 23 2011 CROSSREFS Cf. A001414. Sequence in context: A247712 A030698 A080284 * A071861 A159298 A262118 Adjacent sequences:  A193455 A193456 A193457 * A193459 A193460 A193461 KEYWORD nonn AUTHOR J. M. Bergot, Jul 26 2011 STATUS approved

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Last modified September 30 03:36 EDT 2020. Contains 337434 sequences. (Running on oeis4.)