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.
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
KEYWORD
nonn
AUTHOR
J. M. Bergot, Jul 26 2011
STATUS
approved