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%I #21 Jul 21 2023 17:55:58
%S 2,3,2,5,2,7,2,3,3,11,2,13,4,4,2,17,2,19,3,5,6,23,2,5,7,3,3,29,3,31,2,
%T 7,9,6,2,37,10,8,2,41,4,43,5,3,12,47,2,7,4,10,5,53,2,8,3,11,15,59,3,
%U 61,16,4,2,9,5,67,7,13,4,71,2,73,19,4,7,9,6,79,2,3,21,83,3,11,22,16,4,89,3,10
%N Floor of the average of the prime factors of n with multiplicity.
%F a(p^n)=p, p prime, n >= 1. - _Philippe Deléham_, Nov 23 2008
%F a(n) = floor(A001414(n)/A001222(n)). - _Philippe Deléham_, Nov 24 2008
%t Table[Floor[(Plus@@Times@@@FactorInteger[n])/PrimeOmega[n]], {n, 2, 90}] (* _Alonso del Arte_, May 21 2012 *)
%o (PARI) avg(n) = { local(x,j,ln) for(x=2,n,a=ifactor(x); ln=length(a); print1(floor(sum(j=1,ln,a[j])/ln)",")) } ifactor(n) = \The vector of the prime factors of n with multiplicity. { local(f,j,k,flist); flist=[]; f=Vec(factor(n)); for(j=1,length(f[1]), for(k = 1,f[2][j],flist = concat(flist,f[1][j]) ); ); return(flist) }
%Y Cf. A067629 (rounding instead of flooring), A076690.
%Y This is the floor of A123528/A123529.
%Y Without multiplicity we have A363895.
%Y For prime indices instead of factors we have A363943, triangle A363945.
%Y Positions of first appearances are A364037.
%Y The ceiling is A364156.
%Y Positions of 2's are A364157, for prime indices A363949.
%Y A051293 counts subsets with integer mean, median A000975.
%Y A067538 counts partitions with integer mean, ranks A316413.
%Y A078175 lists numbers with integer mean of prime factors.
%Y Cf. A026905, A326567/A326568, A327473, A327476, A363944, A363948, A363950.
%K easy,nonn
%O 2,1
%A _Cino Hilliard_, Jan 06 2007
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