A187073 Composite squarefree numbers whose average prime factor is a prime number.

21, 33, 57, 69, 85, 93, 105, 129, 133, 145, 177, 195, 205, 213, 217, 231, 237, 249, 253, 265, 309, 393, 417, 445, 465, 469, 483, 489, 493, 505, 517, 553, 565, 573, 597, 609, 627, 633, 645, 663, 669, 685, 697, 753, 781, 793, 813, 817, 861, 865

Offset: 1

Author

Antonio Roldán, Mar 03 2011

Keywords

• nonn

Examples

			195 = 3 * 5 * 13, and the average is (3 +5 +13) / 3 = 21 / 3 = 7, also a prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Mathematica

okQ[n_] := Module[{p, e}, {p, e} = Transpose[FactorInteger[n]]; ! PrimeQ[n] && Max[e] == 1 && PrimeQ[Mean[p]]]; Select[Range[1000], okQ] (* T. D. Noe, Mar 03 2011 *)

PARI

isA187073(n)=my(f=factor(n));#f[,1]>1&vecmax(f[,2])==1&denominator(f=sum(i=1,#f[,1],f[i,1])/#f[,1])==1&isprime(f) \\ Charles R Greathouse IV, Jun 12 2011