来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a326438 Showing 1-1 of 1 %I A326438 %S A326438 1,2,4,6,12,16,32,40,80,120,180,216,432,504,672,840,1680,1920,2880, %T A326438 3240,4320,5184,6048,6720,13440,17920,20480,30720,38400,42240,84480, %U A326438 92160,184320,207360,230400,253440,506880,549120,599040,648960,973440 %N A326438 Number of subsets of {1..n} such that no two elements have the same sorted prime signature. %C A326438 The sorted prime signature (A118914) of a positive integer is the multiset of exponents in its standard factorization into prime numbers. %e A326438 The a(0) = 1 through a(5) = 16 subsets: %e A326438 {} {} {} {} {} {} %e A326438 {1} {1} {1} {1} {1} %e A326438 {2} {2} {2} {2} %e A326438 {1,2} {3} {3} {3} %e A326438 {1,2} {4} {4} %e A326438 {1,3} {1,2} {5} %e A326438 {1,3} {1,2} %e A326438 {1,4} {1,3} %e A326438 {2,4} {1,4} %e A326438 {3,4} {1,5} %e A326438 {1,2,4} {2,4} %e A326438 {1,3,4} {3,4} %e A326438 {4,5} %e A326438 {1,2,4} %e A326438 {1,3,4} %e A326438 {1,4,5} %t A326438 prisig[n_]:=If[n==1,{},Sort[Last/@FactorInteger[n]]]; %t A326438 Table[Length[Select[Subsets[Range[n]],UnsameQ@@prisig/@#&]],{n,0,10}] %Y A326438 Cf. A001221, A001222, A025487, A064839, A085089, A112798, A118914, A124010, A181819, A325263, A325365, A326439, A326441. %K A326438 nonn %O A326438 0,2 %A A326438 _Gus Wiseman_, Jul 06 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE