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 A305025 a(n) = A001221(A004394(n)). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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. LINKS Amiram Eldar, Table of n, a(n) for n = 1..1000 EXAMPLE A004394(8) = 48 = 2^4*3, which has 2 distinct prime factors, so a(8)=2. 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]] CROSSREFS Cf. A001221, A004394, A108602. Sequence in context: A343265 A059396 A108602 * A363743 A085290 A108611 Adjacent sequences: A305022 A305023 A305024 * A305026 A305027 A305028 KEYWORD nonn,easy AUTHOR Michael De Vlieger, Jun 30 2018 STATUS approved

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Last modified May 26 07:52 EDT 2024. Contains 372807 sequences. (Running on oeis4.)