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A036761
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Number of refactorable integers (A033950) of binary order (A029837) n.
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4
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1, 1, 0, 1, 2, 2, 4, 8, 13, 22, 39, 77, 137, 254, 459, 889, 1665, 3175, 6041, 11619, 22319, 42979
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Since for any epsilon d[ n ]<=n^epsilon if n is large enough, a[ n ] does not grow too fast.
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FORMULA
| di[ x_ ] := Divisors[ x ]; ldi[ x_ ] := Length[ Divisors[ x ] ]; md[ x_ ] := MemberQ[ di[ x ], ldi[ x ] ] is used to form counting program line.
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EXAMPLE
| {1} has binary order 0, {2} has binary order 1, no term has binary order 2, {8} has binary order 3, {9,12} have binary order 4, {18,24} have binary order 5,...
The 8 numbers, between 65 and 128 (with binary order 7) which are divided by d(x) (A000005) are 72,80,84,88,96,104,108,128, so a(7)=8.
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MAPLE
| with(numtheory): A036761 := proc(n) local ct, k, lim: if(n=0)then return 1: else ct:=0: lim:=2^n: for k from 2^(n-1)+1 to lim do if(k mod tau(k) = 0)then ct:=ct+1: fi: od: return ct: fi: end: seq(A036761(n), n=0..10); # Nathaniel Johnston, May 04 2011
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CROSSREFS
| A000005, A033950.
Sequence in context: A079092 A039941 A104700 * A042979 A000018 A161905
Adjacent sequences: A036758 A036759 A036760 * A036762 A036763 A036764
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KEYWORD
| nonn,more
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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