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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A084109 A376543 A016105 * A271101 A191683 A032603

Adjacent sequences: A187070 A187071 A187072 * A187074 A187075 A187076

Keyword

nonn

Author

Antonio Roldán, Mar 03 2011

Status

approved