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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[#[[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
Sequence in context: A003679 A079432 A162215 * A324278 A119315 A346256
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 March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)