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%I #17 Aug 02 2022 17:30:48
%S 4,8,9,15,16,20,21,25,27,32,33,35,39,42,44,49,50,51,55,57,60,64,65,68,
%T 69,77,78,81,85,87,91,92,93,95,105,110,111,112,114,115,116,119,121,
%U 123,125,128,129,133,140,141,143,145,155,156,159,161,164,169,170,177,180
%N Composite numbers with an integer arithmetic mean of all prime factors.
%C That is, composite numbers such that the arithmetic mean of their prime factors (counted with multiplicity) is an integer.
%H Amiram Eldar, <a href="/A078177/b078177.txt">Table of n, a(n) for n = 1..10000</a>
%F A001414(a(n)) == 0 modulo A001222(a(n)).
%e 60 = 2*2*3*5: (2+2+3+5)/4 = 3, therefore 60 is a term.
%t Select[Range[200], CompositeQ[#] && IntegerQ[Mean[Flatten[Table[#[[1]], #[[2]]]& /@ FactorInteger[#]]]]&] (* _Jean-François Alcover_, Aug 03 2018 *)
%o (PARI) lista(nn) = {forcomposite(n=1, nn, my(f = factor(n)); if (! (sum(k=1, #f~, f[k,1]*f[k,2]) % vecsum(f[,2])), print1(n, ", ")););} \\ _Michel Marcus_, Feb 22 2016
%Y Cf. A078175, A001222, A100118, A046363, A133620, A133621.
%Y Cf. A133880, A133890, A133900, A133910, A133911, A046346, A134331, A134332, A134333, A134334, A134344, A134376.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Nov 20 2002
%E Edited by _N. J. A. Sloane_, May 30 2008 at the suggestion of _R. J. Mathar_
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