OFFSET

1,1

COMMENTS

All terms are even. (Cf. formula.)

The definition implies that the sum of factors is the sum over the prime factors with multiplicity, as in A001414. - R. J. Mathar, Nov 28 2008

The sum of factors of a semiprime pq is p+q, which can only be prime if {p, q} = {2, odd prime}. Requiring the sum to be prime then implies that the semiprime is twice the lesser of a twin prime pair. - M. F. Hasler, Apr 07 2015

Subsequence of A288814, each term being of the form A288814(p), where p is the greatest of a pair of twin primes. - David James Sycamore, Aug 29 2017

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

a(n)=2*p, with p and 2+p twin primes: a(n)=2*A001359(n).

EXAMPLE

58=2*29 and 2+29 is prime.

MATHEMATICA

Select[Range[2, 3000, 2], !IntegerQ[Sqrt[ # ]]&&Plus@@(Transpose[FactorInteger[ # ]])[[2]]==2&&PrimeQ[Plus@@(Transpose[FactorInteger[ # ]])[[1]]]&]

Select[Range[2, 3000, 2], PrimeOmega[#]==PrimeNu[#]==2&&PrimeQ[Total[ FactorInteger[ #][[;; , 1]]]]&] (* Harvey P. Dale, Apr 10 2023 *)

PROG

(PARI) list(lim)=my(v=List(), p=2); forprime(q=3, lim\2+1, if(q-p==2, listput(v, 2*p)); p=q); Vec(v) \\ Charles R Greathouse IV, Feb 05 2017

CROSSREFS

KEYWORD

easy,nonn

AUTHOR

Zak Seidov, Jun 12 2005

EXTENSIONS

Changed division by 2 to multiplication by 2 in formula related to A001359. - R. J. Mathar, Nov 28 2008

STATUS

approved