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%I #37 May 17 2017 13:47:59
%S 6,4,8,12,16,92,64,144,508,256,1024,3392,8192,3072,13248,19456,114688,
%T 81920,65536,262144,671744,1048576,983040,1835008,5296128,9437184,
%U 16777216,54525952,121634816,201326592,587202560,738197504,3340500992,6710886400,3959422976,4294967296,28991029248,18253611008,68719476736
%N a(n) = smallest number whose arithmetic derivative has exactly n prime factors.
%e a(1) = 6 because 6' = 5;
%e a(2) = 4 because 4' = 4 = 2 * 2;
%e a(3) = 8 because 8' = 12 = 2 * 2 * 3.
%p with(numtheory): P:= proc(q) local k,n; for n from 1 to q do for k from 1 to q do
%p if bigomega(k*add(op(2,p)/op(1,p),p=ifactors(k)[2]))=n then print(k); break; fi;
%p od; od; end: P(10^9);
%t ad[1]=0; ad[n_] := n*Total[ (#1[[2]] / #1[[1]] &) /@ FactorInteger[n]]; a[n_] := Block[{k=2}, While[PrimeOmega@ ad[k] != n, k++]; k]; Array[a, 15] (* _Giovanni Resta_, Mar 22 2017 *)
%Y Cf. A003415.
%K nonn
%O 1,1
%A _Paolo P. Lava_, Mar 21 2017
%E a(29)-a(31) from _Ray Chandler_, Mar 24 2017
%E a(32)-a(33) from _Hans Havermann_, Mar 24 2017
%E a(34)-a(36) from _Hans Havermann_, Mar 26 2017
%E a(37)-a(39) from _Hans Havermann_, May 17 2017
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