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!)
 A324935 Matula-Goebel numbers of rooted trees whose non-leaf terminal subtrees are all different. 12
 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 19, 20, 21, 22, 24, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 42, 43, 44, 48, 51, 52, 53, 56, 57, 58, 59, 62, 64, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 84, 85, 86, 88, 89, 91, 95, 96, 101, 102, 104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Every positive integer has a unique factorization into factors q(i) = prime(i)/i, i > 0. This sequence consists of all numbers where this factorization has all distinct factors, except possibly for any multiplicity of q(1). For example, 22 = q(1)^2 q(2) q(3) q(5) is in the sequence, while 50 = q(1)^3 q(2)^2 q(3)^2 is not. The enumeration of these trees by number of vertices is A324936. LINKS EXAMPLE The sequence of trees together with their Matula-Goebel numbers begins:    1: o    2: (o)    3: ((o))    4: (oo)    5: (((o)))    6: (o(o))    7: ((oo))    8: (ooo)   10: (o((o)))   11: ((((o))))   12: (oo(o))   13: ((o(o)))   14: (o(oo))   16: (oooo)   17: (((oo)))   19: ((ooo))   20: (oo((o)))   21: ((o)(oo))   22: (o(((o))))   24: (ooo(o))   26: (o(o(o)))   28: (oo(oo))   29: ((o((o))))   31: (((((o))))) MATHEMATICA difac[n_]:=If[n==1, {}, With[{i=PrimePi[FactorInteger[n][[1, 1]]]}, Sort[Prepend[difac[n*i/Prime[i]], i]]]]; Select[Range, UnsameQ@@DeleteCases[difac[#], 1]&] CROSSREFS Cf. A000081, A004111, A007097, A061775, A196050, A276625, A290822, A317713. Cf. A324850, A324922, A324923, A324924, A324931, A324934, A324936. Sequence in context: A257500 A121208 A331914 * A328369 A207674 A162722 Adjacent sequences:  A324932 A324933 A324934 * A324936 A324937 A324938 KEYWORD nonn AUTHOR Gus Wiseman, Mar 21 2019 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 April 10 11:35 EDT 2021. Contains 342845 sequences. (Running on oeis4.)