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%I #8 Jun 29 2019 11:32:06
%S 0,1,1,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,
%T 6,6,6,6,6,7,7,7,7,7,7,7,8,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,
%U 9,9,9,10,9,10,10,10,10,10,10,10,10,10,11
%N a(n) = A001221(A004394(n)).
%C Number of distinct prime factors of superabundant numbers.
%C Analogous to A108602 (which instead pertains to A002182, the highly composite numbers).
%C a(23) = 5 while A108602(23) = 4; 23 is the smallest index where this sequence differs from A108602.
%H Amiram Eldar, <a href="/A305025/b305025.txt">Table of n, a(n) for n = 1..1000</a>
%e A004394(8) = 48 = 2^4*3, which has 2 distinct prime factors, so a(8)=2.
%t (* First, convert terms in b-file at A004394 into a list of terms: *)
%t f[w_] := Times @@ Flatten@ {Complement[#1, Union[#2, #3]], Product[Prime@ i, {i, PrimePi@ #}] & /@ #2, Factorial /@ #3} & @@ ToExpression@ {StringSplit[w, _?(! DigitQ@ # &)], StringCases[w, (x : DigitCharacter ..) ~~ "#" :> x], StringCases[w, (x : DigitCharacter ..) ~~ "!" :> x]};
%t s = Map[Which[StringTake[#, 1] == {"#"}, f@ Last@ StringSplit@ Last@ #, StringTake[#, 1] == {}, Nothing, True, ToExpression@ StringSplit[#][[1, -1]]] &, Drop[Import["b004394.txt", "Data"], 3] ];
%t PrimeNu[Take[s, 105]]
%Y Cf. A001221, A004394, A108602.
%K nonn,easy
%O 1,4
%A _Michael De Vlieger_, Jun 30 2018
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