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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..48.
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EXAMPLE
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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.
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MAPLE
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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
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CROSSREFS
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Cf. A001414.
Sequence in context: A214396 A030698 A080284 * A071861 A159298 A173376
Adjacent sequences: A193455 A193456 A193457 * A193459 A193460 A193461
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot, Jul 26 2011
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STATUS
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approved
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