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!)
 A336570 Number of maximal sets of proper divisors d|n, d < n, all belonging to A130091 (numbers with distinct prime multiplicities) and forming a divisibility chain. 7
 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 2, 4, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 4, 1, 2, 2, 1, 2, 3, 1, 2, 2, 3, 1, 5, 1, 2, 2, 2, 2, 3, 1, 4, 1, 2, 1, 4, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization, so a number has distinct prime multiplicities iff all the exponents in its prime signature are distinct. LINKS EXAMPLE The a(n) sets for n = 36, 120, 144, 180 (ones not shown):   {2,18}    {3,12,24}    {2,18,72}       {2,18}   {3,12}    {5,20,40}    {3,9,18,72}     {3,12}   {2,4,12}  {2,4,8,24}   {3,12,24,48}    {5,20}   {3,9,18}  {2,4,8,40}   {3,12,24,72}    {5,45}             {2,4,12,24}  {2,4,8,16,48}   {2,4,12}             {2,4,20,40}  {2,4,8,24,48}   {2,4,20}                          {2,4,8,24,72}   {3,9,18}                          {2,4,12,24,48}  {3,9,45}                          {2,4,12,24,72} MATHEMATICA strsigQ[n_]:=UnsameQ@@Last/@FactorInteger[n]; fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)]; strses[n_]:=If[n==1, {{}}, Join@@Table[Append[#, d]&/@strses[d], {d, Select[Most[Divisors[n]], strsigQ]}]]; Table[Length[fasmax[strses[n]]], {n, 100}] CROSSREFS A336569 is the version for chains containing n. A336571 is the non-maximal version. A000005 counts divisors. A001055 counts factorizations. A007425 counts divisors of divisors. A032741 counts proper divisors. A045778 counts strict factorizations. A071625 counts distinct prime multiplicities. A074206 counts strict chains of divisors from n to 1. A130091 lists numbers with distinct prime multiplicities. A181796 counts divisors with distinct prime multiplicities. A253249 counts chains of divisors. A336422 counts divisible pairs of divisors, both in A130091. A336424 counts factorizations using A130091. A336500 counts divisors of n in A130091 with quotient also in A130091. Cf. A002033, A005117, A098859, A118914, A124010, A305149, A327498, A327523, A336414, A336423, A336425, A336568. Sequence in context: A050320 A333175 A294893 * A121382 A305150 A333145 Adjacent sequences:  A336567 A336568 A336569 * A336571 A336572 A336573 KEYWORD nonn AUTHOR Gus Wiseman, Jul 29 2020 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 September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)