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!)
 A323307 Number of ways to fill a matrix with the parts of a multiset whose multiplicities are the prime indices of n. 11
 1, 1, 2, 4, 2, 6, 3, 12, 18, 12, 2, 36, 4, 10, 20, 72, 2, 60, 4, 40, 60, 24, 3, 120, 80, 14, 360, 120, 4, 240, 2, 240, 42, 32, 70, 720, 6, 27, 112, 480, 2, 210, 4, 84, 420, 40, 4, 1440, 280, 280, 108, 224, 5, 1260, 224, 420, 180, 22, 2, 840, 6, 72, 1680, 2880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This multiset (row n of A305936) is generally not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}. LINKS FORMULA a(n) = A318762(n) * A000005(A056239(n)). EXAMPLE The a(22) = 24 matrices:   [111112] [111121] [111211] [112111] [121111] [211111] .   [111] [111] [111] [112] [121] [211]   [112] [121] [211] [111] [111] [111] .   [11] [11] [11] [11] [12] [21]   [11] [11] [12] [21] [11] [11]   [12] [21] [11] [11] [11] [11] .   [1] [1] [1] [1] [1] [2]   [1] [1] [1] [1] [2] [1]   [1] [1] [1] [2] [1] [1]   [1] [1] [2] [1] [1] [1]   [1] [2] [1] [1] [1] [1]   [2] [1] [1] [1] [1] [1] MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; ptnmats[n_]:=Union@@Permutations/@Select[Union@@(Tuples[Permutations/@#]&/@Map[primeMS, facs[n], {2}]), SameQ@@Length/@#&]; nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]]; Array[Length[ptnmats[Times@@Prime/@nrmptn[#]]]&, 30] CROSSREFS Cf. A007716, A056239, A112798, A120733, A181821, A305936, A318283, A318284, A323295, A323300, A323351. Sequence in context: A182812 A328985 A328196 * A215841 A272327 A212012 Adjacent sequences:  A323304 A323305 A323306 * A323308 A323309 A323310 KEYWORD nonn AUTHOR Gus Wiseman, Jan 13 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 April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)