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

1,1

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

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

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

Adjacent sequences: A187397 A187398 A187399 * A187401 A187402 A187403

Keyword

nonn

Author

Antonio Roldán, Mar 09 2011

Status

approved