The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A327522 Number of factorizations of the n-th prime power A000961(n) into prime powers > 1. 0
 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS FORMULA a(n) = A000041(A001222(A000961(n))). EXAMPLE The a(32) = 5 factorizations of 81:   (3*3*3*3)   (3*3*9)   (3*27)   (9*9)   (81) The a(32) = 5 multiset partitions of the prime indices of 81 into constant multisets:   {{2},{2},{2},{2}}   {{2},{2},{2,2}}   {{2},{2,2,2}}   {{2,2},{2,2}}   {{2,2,2,2}} 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, #]&]}]]; y=Select[Range[nn], PrimePowerQ]; Table[Length[facsusing[Rest[y], n]], {n, y}] CROSSREFS See link for additional cross-references. Cf. A000961, A001055, A001222, A001597, A005117, A007916. Sequence in context: A248641 A282934 A273619 * A034003 A306722 A168508 Adjacent sequences:  A327519 A327520 A327521 * A327523 A327524 A327525 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 23 10:45 EDT 2021. Contains 345397 sequences. (Running on oeis4.)