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 A302242 Total weight of the n-th multiset multisystem. Totally additive with a(prime(n)) = Omega(n). 178
 0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 1, 1, 2, 2, 2, 0, 1, 2, 3, 1, 3, 1, 2, 1, 2, 2, 3, 2, 2, 2, 1, 0, 2, 1, 3, 2, 3, 3, 3, 1, 1, 3, 2, 1, 3, 2, 2, 1, 4, 2, 2, 2, 4, 3, 2, 2, 4, 2, 1, 2, 3, 1, 4, 0, 3, 2, 1, 1, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 1, 4, 1, 1, 3, 2, 2, 3, 1, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS A multiset multisystem is a finite multiset of finite multisets of positive integers. The n-th multiset multisystem is constructed by factoring n into prime numbers and then factoring each prime index into prime numbers and taking their prime indices. This produces a unique multiset multisystem for each n, and every possible multiset multisystem is so constructed as n ranges over all positive integers. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..65536 EXAMPLE Sequence of finite multisets of finite multisets of positive integers begins: (), (()), ((1)), (()()), ((2)), (()(1)), ((11)), (()()()), ((1)(1)), (()(2)), ((3)), (()()(1)), ((12)), (()(11)), ((1)(2)), (()()()()), ((4)), (()(1)(1)), ((111)), (()()(2)). MAPLE with(numtheory): a:= n-> add(add(j[2], j=ifactors(pi(i[1]))[2])*i[2], i=ifactors(n)[2]): seq(a(n), n=1..100);  # Alois P. Heinz, Sep 07 2018 MATHEMATICA primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Table[Total[PrimeOmega/@primeMS[n]], {n, 100}] CROSSREFS Cf. A001222, A003963, A007716, A034691, A056239, A061775, A063834, A096443, A249620, A255397, A255906, A275024, A279789, A281113, A299757, A302243. Sequence in context: A117447 A328775 A053250 * A236627 A116664 A295672 Adjacent sequences:  A302239 A302240 A302241 * A302243 A302244 A302245 KEYWORD nonn AUTHOR Gus Wiseman, Apr 03 2018 STATUS approved

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Last modified April 6 22:23 EDT 2020. Contains 333291 sequences. (Running on oeis4.)