A193458 Union of A071863 and A071861.

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

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

Table of n, a(n) for n=1..48.

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