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 A285573 Number of finite nonempty sets of pairwise indivisible divisors of n. 45
 1, 2, 2, 3, 2, 5, 2, 4, 3, 5, 2, 9, 2, 5, 5, 5, 2, 9, 2, 9, 5, 5, 2, 14, 3, 5, 4, 9, 2, 19, 2, 6, 5, 5, 5, 19, 2, 5, 5, 14, 2, 19, 2, 9, 9, 5, 2, 20, 3, 9, 5, 9, 2, 14, 5, 14, 5, 5, 2, 49, 2, 5, 9, 7, 5, 19, 2, 9, 5, 19, 2, 34, 2, 5, 9, 9, 5, 19, 2, 20, 5, 5, 2, 49, 5, 5, 5, 14, 2, 49, 5, 9, 5, 5, 5, 27, 2, 9, 9, 19 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Robert Israel, Apr 21 2017: (Start) If n = p^k for prime p, a(n) = k+1. If n = p^j*q^k for distinct primes p,q, a(n) = binomial(j+k+2,j+1)-1. (End) LINKS EXAMPLE The a(12)=9 sets are: {1}, {2}, {3}, {4}, {6}, {12}, {2,3}, {3,4}, {4,6}. MAPLE g:= proc(S) local x, Sx; option remember;    if nops(S) = 0 then return {{}} fi;    x:= S[1];    Sx:= subsop(1=NULL, S);    procname(Sx) union map(t -> t union {x}, procname(remove(s -> s mod x = 0 or x mod s = 0, Sx))) end proc: f:= proc(n) local F, D;   F:= ifactors(n)[2];   D:= numtheory:-divisors(mul(ithprime(i)^F[i, 2], i=1..nops(F)));   nops(g(D)) - 1; end proc: map(f, [\$1..100]); # Robert Israel, Apr 21 2017 MATHEMATICA nn=50; stableSets[u_, Q_]:=If[Length[u]===0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r===w||Q[r, w]||Q[w, r]], Q]]]]; Table[Length[Rest[stableSets[Divisors[n], Divisible]]], {n, 1, nn}] CROSSREFS Cf. A006126, A048143, A076078, A076413, A198085, A285572. Sequence in context: A343654 A100565 A244098 * A325339 A010846 A073023 Adjacent sequences:  A285570 A285571 A285572 * A285574 A285575 A285576 KEYWORD nonn AUTHOR Gus Wiseman, Apr 21 2017 STATUS approved

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Last modified June 21 17:44 EDT 2021. Contains 345365 sequences. (Running on oeis4.)