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 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 (list; graph; refs; listen; history; text; internal format)
 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[#[], {#[]}]&/@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

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Last modified April 21 11:06 EDT 2021. Contains 343150 sequences. (Running on oeis4.)