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A324930
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Total weight of the multiset of multisets of multisets with MMM number n. Totally additive with a(prime(n)) = A302242(n).
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3
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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, 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, 2, 1, 1, 0, 3, 1, 2, 0, 1, 1, 1, 1, 0, 2, 2, 0, 3, 2, 1
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OFFSET
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1,17
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The sequence of all finite multisets of finite multisets of finite multisets of positive integers begins (o is the empty multiset):
1: o
2: (o)
3: ((o))
4: (oo)
5: (((1)))
6: (o(o))
7: ((oo))
8: (ooo)
9: ((o)(o))
10: (o((1)))
11: (((2)))
12: (oo(o))
13: ((o(1)))
14: (o(oo))
15: ((o)((1)))
16: (oooo)
17: (((11)))
18: (o(o)(o))
19: ((ooo))
20: (oo((1)))
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MATHEMATICA
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fi[n_]:=If[n==1, {}, FactorInteger[n]];
Table[Total[Cases[fi[n], {p_, k_}:>k*Total[Cases[fi[PrimePi[p]], {q_, j_}:>j*PrimeOmega[PrimePi[q]]]]]], {n, 60}]
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CROSSREFS
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Cf. A000081, A000720, A001222, A050338, A056239, A112798, A301595, A302242, A318564, A318565, A318566, A324928.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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