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A134344
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Composite numbers such that the arithmetic mean of their prime factors (counted with multiplicity) is prime.
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28
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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
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A000040, A001222, A100118, A046363, A133620, A133621, A133880, A133890, A133900, A133910, A133911, A046346, A134331, A134332, A134333, A134334.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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