cp's OEIS Frontend

A324930 Total weight of the multiset of multisets of multisets with MMM number n. Totally additive with a(prime(n)) = A302242(n).

%I A324930 #5 Mar 22 2019 00:32:24
%S A324930 0,0,0,0,1,0,0,0,0,1,1,0,1,0,1,0,2,0,0,1,0,1,2,0,2,1,0,0,1,1,1,0,1,2,
%T A324930 1,0,1,0,1,1,2,0,2,1,1,2,2,0,0,2,2,1,0,0,2,0,0,1,1,1,2,1,0,0,2,1,3,2,
%U A324930 2,1,1,0,3,1,2,0,1,1,1,1,0,2,2,0,3,2,1
%N A324930 Total weight of the multiset of multisets of multisets with MMM number n. Totally additive with a(prime(n)) = A302242(n).
%C A324930 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The finite multiset of finite multisets of finite multisets of positive integers with MMM number n is obtained by factoring n into prime numbers, then factoring each of their prime indices into prime numbers, then factoring each of their prime indices into prime numbers, and finally taking their prime indices.
%e A324930 The sequence of all finite multisets of finite multisets of finite multisets of positive integers begins (o is the empty multiset):
%e A324930    1: o
%e A324930    2: (o)
%e A324930    3: ((o))
%e A324930    4: (oo)
%e A324930    5: (((1)))
%e A324930    6: (o(o))
%e A324930    7: ((oo))
%e A324930    8: (ooo)
%e A324930    9: ((o)(o))
%e A324930   10: (o((1)))
%e A324930   11: (((2)))
%e A324930   12: (oo(o))
%e A324930   13: ((o(1)))
%e A324930   14: (o(oo))
%e A324930   15: ((o)((1)))
%e A324930   16: (oooo)
%e A324930   17: (((11)))
%e A324930   18: (o(o)(o))
%e A324930   19: ((ooo))
%e A324930   20: (oo((1)))
%t A324930 fi[n_]:=If[n==1,{},FactorInteger[n]];
%t A324930 Table[Total[Cases[fi[n],{p_,k_}:>k*Total[Cases[fi[PrimePi[p]],{q_,j_}:>j*PrimeOmega[PrimePi[q]]]]]],{n,60}]
%Y A324930 Cf. A000081, A000720, A001222, A050338, A056239, A112798, A301595, A302242, A318564, A318565, A318566, A324928.
%K A324930 nonn
%O A324930 1,17
%A A324930 _Gus Wiseman_, Mar 21 2019