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A187400
Semiprimes with a semiprime average of the two factors.
1
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
OFFSET
1,1
COMMENTS
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.
LINKS
EXAMPLE
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.
MATHEMATICA
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]]
PROG
(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
CROSSREFS
Cf. A001358.
Sequence in context: A268463 A108668 A201018 * A162280 A290781 A340449
KEYWORD
nonn
AUTHOR
Antonio Roldán, Mar 09 2011
STATUS
approved