

A134344


Composite numbers such that the arithmetic mean of their prime factors (counted with multiplicity) is prime.


28



4, 8, 9, 16, 20, 21, 25, 27, 32, 33, 44, 49, 57, 60, 64, 68, 69, 81, 85, 93, 105, 112, 116, 121, 125, 128, 129, 133, 145, 156, 169, 177, 180, 188, 195, 205, 212, 213, 217, 220, 231, 237, 243, 249, 253, 256, 265, 272, 275, 289, 297, 309, 332, 336, 343, 356, 361
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OFFSET

1,1


COMMENTS

Originally, the definition started with "Nonprime numbers ...". This may be misleading, since 1 is also nonprime, but has no prime factors.  Hieronymus Fischer, May 05 2013


LINKS

Harvey P. Dale and Hieronymus Fischer, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)


EXAMPLE

a(1) = 4, since 4 = 2*2 and the arithmetic mean (2+2)/2 = 2 is prime.
a(5) = 20, since 20 = 2*2*5 and the arithmetic mean (2+2+5)/3 = 3 is prime.


MATHEMATICA

ampfQ[n_]:=PrimeQ[Mean[Flatten[Table[#[[1]], {#[[2]]}]&/@FactorInteger[ n]]]]; nn=400; Select[Complement[Range[nn], Prime[Range[ PrimePi[nn]]]], ampfQ] (* Harvey P. Dale, Nov 06 2012 *)


PROG

(PARI) is(n)=if(n<4, return(0)); my(f=factor(n), s=sum(i=1, #f~, f[i, 1]*f[i, 2])/sum(i=1, #f~, f[i, 2])); (#f~>1  f[1, 2]>1) && denominator(s)==1 && isprime(s) \\ Charles R Greathouse IV, Sep 14 2015


CROSSREFS

Cf. A000040, A001222, A100118, A046363, A133620, A133621, A133880, A133890, A133900, A133910, A133911, A134330, A134331, A134332, A134333, A134334.
Sequence in context: A003679 A079432 A162215 * A324278 A119315 A010390
Adjacent sequences: A134341 A134342 A134343 * A134345 A134346 A134347


KEYWORD

nonn


AUTHOR

Hieronymus Fischer, Oct 23 2007


EXTENSIONS

Definition clarified by Hieronymus Fischer, May 05 2013


STATUS

approved



