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 A108605 Semiprimes with prime sum of factors: twice the lesser of the twin prime pairs. 13
 6, 10, 22, 34, 58, 82, 118, 142, 202, 214, 274, 298, 358, 382, 394, 454, 478, 538, 562, 622, 694, 838, 862, 922, 1042, 1138, 1198, 1234, 1282, 1318, 1618, 1642, 1654, 1714, 1762, 2038, 2062, 2098, 2122, 2182, 2302, 2458, 2554, 2578, 2602, 2638, 2854, 2902 (list; graph; refs; listen; history; text; internal format)
 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&&PrimeQ[Plus@@(Transpose[FactorInteger[ # ]])[]]&] 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 Cf. A001358 semiprimes, A001359 lesser of twin primes, A101605 3-almost primes, A108606 semiprimes with prime sum of digits, A108607 intersection of A108605 and A108606. Sequence in context: A255746 A082917 A001172 * A216049 A063765 A085712 Adjacent sequences:  A108602 A108603 A108604 * A108606 A108607 A108608 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

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Last modified August 25 05:40 EDT 2019. Contains 326319 sequences. (Running on oeis4.)