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A327520
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Number of factorizations of the n-th stable number A316476(n) into stable numbers > 1.
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0
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1, 1, 2, 1, 1, 3, 2, 1, 1, 2, 5, 1, 1, 1, 2, 3, 1, 1, 7, 2, 2, 1, 1, 1, 4, 1, 2, 2, 1, 2, 1, 1, 11, 1, 2, 1, 1, 4, 2, 1, 5, 1, 2, 1, 2, 2, 2, 1, 4, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 15, 1, 7, 1, 1, 2, 2, 2, 1, 1, 4, 2, 1, 2, 1, 5, 1, 2, 1, 4, 2, 1, 1, 2, 1, 1, 1
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OFFSET
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1,3
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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. A number is stable if its distinct prime indices are pairwise indivisible. Stable numbers are listed in A316476.
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LINKS
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Table of n, a(n) for n=1..86.
Gus Wiseman, Sequences counting and encoding certain classes of multisets
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EXAMPLE
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The a(26) = 4 factorizations of 45 into stable numbers:
(3*3*5)
(3*15)
(5*9)
(45)
The a(201) = 11 multiset partitions of the prime indices of 495 into stable multisets:
{{2},{2},{3},{5}}
{{2},{2},{3,5}}
{{2},{3},{2,5}}
{{2},{5},{2,3}}
{{2},{2,3,5}}
{{3},{2,2},{5}}
{{3},{2,2,5}}
{{2,2},{3,5}}
{{5},{2,2,3}}
{{2,3},{2,5}}
{{2,2,3,5}}
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MATHEMATICA
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nn=100;
facsusing[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsusing[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
y=Select[Range[nn], stableQ[PrimePi/@First/@FactorInteger[#], Divisible]&];
Table[Length[facsusing[Rest[y], n]], {n, y}]
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CROSSREFS
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See link for additional cross-references.
Cf. A001055, A303362, A305149.
Sequence in context: A254111 A234246 A006375 * A184441 A172279 A164953
Adjacent sequences: A327517 A327518 A327519 * A327521 A327522 A327523
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Sep 15 2019
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STATUS
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approved
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