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A330098
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Number of distinct multisets of multisets that can be obtained by permuting the vertices of the multiset of multisets with MM-number n.
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34
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2
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OFFSET
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1,35
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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 multiset of multisets with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset of multisets with MM-number 78 is {{},{1},{1,2}}.
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LINKS
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EXAMPLE
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The vertex-permutations of {{1,2},{2,3,3}} are:
{{1,2},{1,3,3}}
{{1,2},{2,3,3}}
{{1,3},{1,2,2}}
{{1,3},{2,2,3}}
{{2,3},{1,1,2}}
{{2,3},{1,1,3}}
so a(4927) = 6.
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]], i}, {i, Length[p]}])], {p, Permutations[Union@@m]}]];
Table[Length[graprms[primeMS/@primeMS[n]]], {n, 100}]
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CROSSREFS
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Cf. A001055, A003238, A007716, A055621, A056239, A112798, A302242, A303975, A322847, A330194, A330218, A330223, A330227, A330236.
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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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