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!)
 A336569 Number of maximal strict chains of divisors from n to 1 using elements of A130091 (numbers with distinct prime multiplicities). 12
 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 3, 1, 0, 1, 2, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 3, 1, 0, 1, 2, 2, 0, 1, 4, 1, 2, 0, 2, 1, 3, 0, 3, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 1, 2, 0, 0, 1, 5, 1, 0, 2, 2, 0, 0, 1, 4, 1, 0, 1, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 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) chains for n = 12, 72, 144, 192 (ones not shown):   12/3    72/18/2       144/72/18/2       192/96/48/24/12/3   12/4/2  72/18/9/3     144/72/18/9/3     192/64/32/16/8/4/2           72/24/12/3    144/48/24/12/3    192/96/32/16/8/4/2           72/24/8/4/2   144/72/24/12/3    192/96/48/16/8/4/2           72/24/12/4/2  144/48/16/8/4/2   192/96/48/24/8/4/2                         144/48/24/8/4/2   192/96/48/24/12/4/2                         144/72/24/8/4/2                         144/48/24/12/4/2                         144/72/24/12/4/2 MATHEMATICA strsigQ[n_]:=UnsameQ@@Last/@FactorInteger[n]; fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)]; strchs[n_]:=If[n==1, {{}}, If[!strsigQ[n], {}, Join@@Table[Prepend[#, d]&/@strchs[d], {d, Select[Most[Divisors[n]], strsigQ]}]]]; Table[Length[fasmax[strchs[n]]], {n, 100}] CROSSREFS A336423 is the non-maximal version. A336570 is the version for chains not necessarily containing n. A000005 counts divisors. A001055 counts factorizations. A001222 counts prime factors with multiplicity. 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. A336571 counts divisor sets of elements of A130091. Cf. A002033, A005117, A098859, A118914, A124010, A305149, A327498, A327523, A336414, A336425, A336500, A336568. Sequence in context: A340653 A334744 A136567 * A324904 A109708 A035468 Adjacent sequences:  A336566 A336567 A336568 * A336570 A336571 A336572 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 June 16 12:29 EDT 2021. Contains 345057 sequences. (Running on oeis4.)