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A187400
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Semiprimes with a semiprime average of the two factors.
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1
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15, 35, 51, 65, 77, 91, 115, 123, 141, 161, 185, 187, 201, 209, 219, 221, 235, 259, 267, 301, 305, 321, 339, 341, 355, 365, 377, 381, 403, 413, 427, 437, 451, 453, 481, 485, 497, 501, 537, 545, 589, 649, 667, 681, 689, 699, 717, 721, 723, 737, 745, 749, 763, 789, 835, 843, 849, 893, 901, 905
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OFFSET
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1,1
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COMMENTS
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The definition is similar to A115585, but considering the arithmetic mean, not the sum of the factors.
Even semiprimes, A100484, are not in the sequence, because (with the exception of 4) the average of their factors is not an integer.
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LINKS
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EXAMPLE
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The semiprime 187=11*17 is in the sequence, because the average (11+17)/2=14 = 2*7 is semiprime.
The semiprime 267=3*89 is in the sequence because the average (3+89)/2=46=2*23 is semiprime.
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MATHEMATICA
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semiPrimeQ[n_] := Total[FactorInteger[n]][[2]] == 2; Reap[Do[{p, e} = Transpose[FactorInteger[n]]; If[Total[e] == 2 && semiPrimeQ[Total[p]/2], Sow[n]], {n, 1000}]][[2, 1]]
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PROG
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(PARI)sopf(n)= { local(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s) }
averg(n)={local(s); s=sopf(n)/omega(n); return(s)}
{ for (n=4, 10^3, m=averg(n); if(bigomega(n)==2, if(m==floor(m)&&bigomega(m)==2, print1(n, ", ")))) }
// Antonio Roldán, Oct 15 2012
(PARI) list(lim)=my(v=List()); forprime(p=3, lim\3, forprime(q=3, min(p-2, lim\p), if(bigomega((p+q)/2)==2, listput(v, p*q)))); Set(v) \\ Charles R Greathouse IV, Oct 16 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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