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%I #20 Aug 02 2022 17:29:10
%S 4,8,9,16,20,21,25,27,32,33,44,49,57,60,64,68,69,81,85,93,105,112,116,
%T 121,125,128,129,133,145,156,169,177,180,188,195,205,212,213,217,220,
%U 231,237,243,249,253,256,265,272,275,289,297,309,332,336,343,356,361
%N Composite numbers such that the arithmetic mean of their prime factors (counted with multiplicity) is prime.
%C 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
%H Harvey P. Dale and Hieronymus Fischer, <a href="/A134344/b134344.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from _Harvey P. Dale_)
%e a(1) = 4, since 4 = 2*2 and the arithmetic mean (2+2)/2 = 2 is prime.
%e a(5) = 20, since 20 = 2*2*5 and the arithmetic mean (2+2+5)/3 = 3 is prime.
%t 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 *)
%o (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
%Y Cf. A000040, A001222, A100118, A046363, A133620, A133621, A133880, A133890, A133900, A133910, A133911, A046346, A134331, A134332, A134333, A134334.
%K nonn
%O 1,1
%A _Hieronymus Fischer_, Oct 23 2007
%E Definition clarified by _Hieronymus Fischer_, May 05 2013
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