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%I #28 May 01 2018 04:13:12
%S 2,5,81,10742,10130527,1041972864,23292549600
%N Numbers k such that the average of all distinct prime factors of all positive integers <= k is an integer.
%C Numbers k such that A013939(k)|A024924(k).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%e 5 is in the sequence because the distinct prime factors of 2, 3, 4, and 5 are 2, 3, 2 and 5 respectively and their average (2 + 3 + 2 + 5) / 4 = 3 is an integer. - _David A. Corneth_, Apr 26 2018
%t s = t = 0; k = 2; lst = {}; While[k < 1000000000, p = #[[1]] & /@ FactorInteger@ k; s = s + Plus @@ p; t = t + Length@ p; If[ Mod[s, t] == 0, AppendTo[lst, k]]; k++]; lst (* _Robert G. Wilson v_, Apr 26 2018 *)
%Y Cf. A001221, A008472, A013939, A024924, A078174, A078175, A226647, A284755, A303480.
%K nonn,more
%O 1,1
%A _Ilya Gutkovskiy_, Apr 24 2018
%E a(5) from _Daniel Suteu_, Apr 24 2018
%E a(6)-a(7) from _Giovanni Resta_, Apr 26 2018
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