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A175245
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Let S be the set of distinct positive integers whose binary representations are substrings in the binary representation of n. a(n) = the number of elements of S that are coprime to all other elements of S.
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2
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1, 2, 2, 1, 3, 1, 3, 1, 2, 1, 5, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 2, 7, 1, 2, 1, 4, 1, 4, 1, 3, 1, 2, 1, 4, 1, 3, 1, 3, 1, 3, 1, 3, 2, 2, 3, 6, 1, 3, 1, 3, 1, 2, 3, 4, 1, 2, 1, 6, 1, 4, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4, 1, 2, 1, 3, 1, 4, 2, 4, 1, 3, 1, 4, 1, 1, 1, 4, 2, 2, 1, 1, 3, 5, 3, 7, 1, 2, 1, 2, 1, 3, 2, 5, 1, 2
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OFFSET
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1,2
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LINKS
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EXAMPLE
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27 in binary is 11011. S = (1 (1 in binary), 2 (10 in binary), 3 (11 in binary), 5 (101 in binary), 6 (110 in binary), 11 (1011 in binary), 13 (1101 in binary), 27 (11011 in binary)). Note that all of the binary representations of the elements of S are substrings in 11011. 1 is coprime to all other elements of S. 2 is not coprime to 6. 3 is not coprime to 6 or 27. 5 is coprime to all other elements of S. 6 is not coprime to 2, 3 or 27. 11 is coprime to all other elements. 13 is coprime to all other elements. And 27 is not coprime to 3 or 6. So there are 4 elements that are each coprime to all other elements, thus a(27) = 4.
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MAPLE
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iscopr := proc(n, L) for i in L do if i<> n and gcd(n, i) <> 1 then return 0; end if; end do: return 1; end proc:
rebase := proc(L, b) local i ; add(op(i, L)*b^(i-1), i=1..nops(L)) ; end proc:
A175245 := proc(n) ndgs := convert(n, base, 2) ; S := {} ; for dig1 from 1 to nops(ndgs) do for dig2 from dig1 to nops(ndgs) do if op(dig2, ndgs) <> 0 then S := S union { [op(dig1..dig2, ndgs)] } ; fi ; end do: end do: Sl := [] ; for subd in S do Sl := [op(Sl), rebase(subd, 2) ] ; end do: a := 0 ; for subd in Sl do a := a+ iscopr(subd, Sl); end do: a ; end proc:
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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