

A187073


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


6



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
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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: A280262 A084109 A016105 * A271101 A191683 A032603
Adjacent sequences: A187070 A187071 A187072 * A187074 A187075 A187076


KEYWORD

nonn


AUTHOR

Antonio Roldán, Mar 03 2011


STATUS

approved



