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!)
 A305566 Number of finite sets of relatively prime positive integers > 1 with least common multiple n. 12
 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 10, 0, 2, 2, 0, 0, 10, 0, 10, 2, 2, 0, 44, 0, 2, 0, 10, 0, 84, 0, 0, 2, 2, 2, 122, 0, 2, 2, 44, 0, 84, 0, 10, 10, 2, 0, 184, 0, 10, 2, 10, 0, 44, 2, 44, 2, 2, 0, 1590, 0, 2, 10, 0, 2, 84, 0, 10, 2, 84, 0, 1156, 0, 2, 10, 10, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS From Robert Israel, Jun 06 2018: (Start) a(n) depends only on the prime signature of n. If n is in A000961, a(n)=0. If n is in A006881, a(n)=2. (End) If n = p^k*q, where p and q are distinct primes and k >= 1, then a(n) = 3*4^(k-1)-2^(k-1). - Robert Israel, Jun 07 2018 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE The a(12) = 10 sets: {3,4}, {2,3,4}, {2,3,12}, {3,4,6}, {3,4,12}, {2,3,4,6}, {2,3,4,12}, {2,3,6,12}, {3,4,6,12}, {2,3,4,6,12}. MAPLE f:= proc(n) g(sort(map(t -> t[2], ifactors(n)[2]))) end proc: f(1):= 0: g:= proc(L) option remember;   local nL, Cands, nC, Cons, i;   nL:= nops(L);   Cands:= [[]];   for i from 1 to nL do     Cands:= [seq(seq([op(s), t], t=0..L[i]), s=Cands)];   od:   Cands:= remove(t -> max(t)=0, Cands);   nC:= nops(Cands);   Cons:= [seq(select(t -> Cands[t][i]=0, {\$1..nC}), i=1..nL),           seq(select(t -> Cands[t][i]=L[i], {\$1..nC}), i=1..nL)];   h(Cons, {\$1..nC}) end proc: h:= proc(Cons, Cands)   local t, i, Consi, Candsi;   if Cons = [] then return 2^nops(Cands) fi;   t:= 0;   for i from 1 to nops(Cons[1]) do     Consi:= map(proc(t) if member(Cons[1][i], t) then NULL else t minus Cons[1][1..i-1] fi end proc, Cons[2..-1]);     if member({}, Consi) then next fi;     Candsi:= Cands minus Cons[1][1..i];     t:= t + procname(Consi, Candsi)   od;   t end proc: map(f, [\$1..100]); # Robert Israel, Jun 07 2018 MATHEMATICA Table[Length[Select[Subsets[Rest[Divisors[n]]], And[GCD@@#==1, LCM@@#==n]&]], {n, 100}] CROSSREFS Cf. A000961, A006881, A076078, A181819, A281116, A285572, A290103, A304818, A305563, A305564, A305565, A305567. Sequence in context: A333783 A088886 A317636 * A326813 A137347 A024941 Adjacent sequences:  A305563 A305564 A305565 * A305567 A305568 A305569 KEYWORD nonn AUTHOR Gus Wiseman, Jun 05 2018 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 22 22:24 EDT 2020. Contains 337291 sequences. (Running on oeis4.)