A187400 Semiprimes with a semiprime average of the two factors.

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

Author

Antonio Roldán, Mar 09 2011

Keywords

• nonn

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.

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A100484, A115585.

Programs

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]]

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