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0, 1, 3, 2, 7, 5, 15, 4, 6, 11, 31, 9, 63, 23, 13, 8, 127, 10, 255, 19, 27, 47, 511, 17, 14, 95, 12, 39, 1023, 21, 2047, 16, 55, 191, 29, 18, 4095, 383, 111, 35, 8191, 43, 16383, 79, 25, 767, 32767, 33, 30, 22, 223, 159, 65535, 20, 59, 71, 447
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OFFSET
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1,3
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COMMENTS
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Note the indexing.
a(n) (n>=2) can be obtained by the composition of a bijection between {2,3,4,...} and the set of integer partitions and a bijection between the set of integer partitions and {1,2,3,4,...}. Explanation on the example n=18. Write 18 = 3*3*2 = 2'*2'*1', where m' = m-th prime. Consider the partition p = (2,2,1) and let b denote the southeast border of the Ferrers board of p. Form a binary number by replacing each east step of b by 1 and each north step of b, with the exception of the last one, by 0: 1010. Its value is a(18) = 10. - Emeric Deutsch, Sep 08 2016.
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LINKS
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FORMULA
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As a composition of other permutations:
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MAPLE
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a:= proc(n) local i, l, r; r, l:= 0, [0, sort(map(i->
numtheory[pi](i[1])$i[2], ifactors(n)[2]))[]];
for i to nops(l)-1 do
r:= 2*((x-> 2*x+1)@@(l[i+1]-l[i]))(r)
od; r/2
end:
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MATHEMATICA
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Table[Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[ Table[ 2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]] &[If[n == 1, 1, Module[{l = #, m = 0}, Times @@ Power @@@ Table[l -= m; l = DeleteCases[l, 0]; {Prime@ Length@ l, m = Min@ l}, Length@ Union@ l]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ FactorInteger@ n]]], {n, 57}] (* Michael De Vlieger, Sep 08 2016, after JungHwan Min at A122111 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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