

A108605


Semiprimes with prime sum of factors: twice the lesser of the twin prime pairs.


12



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
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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


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]]]&]


PROG

(PARI) list(lim)=my(v=List(), p=2); forprime(q=3, lim\2+1, if(qp==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 3almost 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



