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

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, 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, 9, 9, 9, 10, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11

Offset: 1

Author

Michael De Vlieger, Jun 30 2018

Keywords

• nonn
• easy

Comments

Number of distinct prime factors of superabundant numbers.

Analogous to A108602 (which instead pertains to A002182, the highly composite numbers).

a(23) = 5 while A108602(23) = 4; 23 is the smallest index where this sequence differs from A108602.

Examples

			A004394(8) = 48 = 2^4*3, which has 2 distinct prime factors, so a(8)=2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001221, A004394, A108602.

Programs

Mathematica

(* First, convert terms in b-file at A004394 into a list of terms: *)
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]};
s = Map[Which[StringTake[#, 1] == {"#"}, f@ Last@ StringSplit@ Last@ #, StringTake[#, 1] == {}, Nothing, True, ToExpression@ StringSplit[#][[1, -1]]] &, Drop[Import["b004394.txt", "Data"], 3] ];
PrimeNu[Take[s, 105]]