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%I #18 Mar 17 2019 02:06:49
%S 5,44,51,54,90,328,390,423,608,1679,1805,1825,2000,2294,2448,2755,
%T 2847,3008,3103,3145,3289,3354,3509,3737,3887,4929,5695,6024,6344,
%U 7080,8509,8949,9085,9379,9453,9675,9685,10286,10584,10730,10787,10933,11725,12035,12193,12462,12499,12564
%N Union of A071863 and A071861.
%C 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.
%e 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.
%p A001414 := proc(n) add( op(1,d)*op(2,d), d = ifactors(n)[2]) ; end proc:
%p 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:
%p 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:
%p isA193458 := proc(n) isA071863(n) or isA071861(n) ; end proc:
%p for n from 2 to 20000 do if isA193458(n) then printf("%d,",n); end if; end do: # _R. J. Mathar_, Aug 23 2011
%Y Cf. A001414.
%K nonn
%O 1,1
%A _J. M. Bergot_, Jul 26 2011
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