cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A305025 a(n) = A001221(A004394(n)).

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