The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A327520 Number of factorizations of the n-th stable number A316476(n) into stable numbers > 1. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. LINKS EXAMPLE 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}} MATHEMATICA 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}] CROSSREFS See link for additional cross-references. Cf. A001055, A303362, A305149. Sequence in context: A254111 A234246 A006375 * A184441 A172279 A348285 Adjacent sequences: A327517 A327518 A327519 * A327521 A327522 A327523 KEYWORD nonn AUTHOR Gus Wiseman, Sep 15 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 30 12:26 EST 2023. Contains 359943 sequences. (Running on oeis4.)