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 A281145 Number of same-trees of weight n. 30
 1, 2, 2, 6, 2, 14, 2, 54, 10, 38, 2, 494, 2, 134, 42, 4470, 2, 3422, 2, 10262, 138, 2054, 2, 490926, 34, 8198, 1514, 314294, 2, 628318, 2, 30229110, 2058, 131078, 162, 150147342, 2, 524294, 8202, 628073814, 2, 109952254, 2, 371210294, 207370, 8388614, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A same-tree is either: (case 1) a positive integer, or (case 2) a finite sequence of two or more same-trees all having the same weight, where the weight in case 2 is the sum of weights. LINKS G. C. Greubel, Table of n, a(n) for n = 1..4000 FORMULA a(n) = 1 + Sum a(d)^(n/d) where the sum is over divisors less than n. EXAMPLE The a(6)=14 same-trees are: 6, (33), (222), (3(111)), ((111)3), (22(11)), (2(11)2), ((11)22), (2(11)(11)), ((11)2(11)), ((11)(11)2), ((111)(111)), ((11)(11)(11)), (111111). The a(9)=10 same-trees are: 9, (333), (33(111)), (3(111)3), ((111)33), (3(111)(111)), ((111)3(111)), ((111)(111)3), ((111)(111)(111)), (111111111). MATHEMATICA a[n_]:=1+DivisorSum[n, b[#]^(n/#)&]-b[n]/.b->a; Array[a, 47] PROG (PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + sumdiv(n, d, v[n/d]^d)); v} \\ Andrew Howroyd, Aug 20 2018 CROSSREFS Cf. A196545, A260685, A273873, A275870, A006241. Sequence in context: A249631 A055934 A096217 * A098555 A057562 A102628 Adjacent sequences:  A281142 A281143 A281144 * A281146 A281147 A281148 KEYWORD nonn AUTHOR Gus Wiseman, Jan 15 2017 STATUS approved

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Last modified February 22 05:49 EST 2020. Contains 332116 sequences. (Running on oeis4.)