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A065413
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Number of positive solutions to "numbers that are n times their number of binary 1's".
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7
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 0, 0, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 1, 2, 1, 1, 1, 1, 3, 0, 1, 0, 0, 1, 0, 2, 2, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 1, 1, 2, 1, 0, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 3, 1, 0, 0, 1, 0, 0, 1, 0, 2, 1, 0, 0, 2
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OFFSET
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1,23
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COMMENTS
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Equivalently, this is the number of ways to write n as an arithmetic mean of distinct powers of 2. [Brian Kell, Mar 01 2009]
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LINKS
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EXAMPLE
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a(23)=3 since 69, 92 and 115 are written in binary as 1000101, 1011100 and 1110011 and 69=23*3, 92=23*4 and 115=23*5.
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MAPLE
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N:= 1000: # to get a(1) to a(N)
A:= Vector(N):
for x from 1 while x/(1+ilog2(x)) <= N do
v:= x/convert(convert(x, base, 2), `+`);
if v::integer and v <= N then
A[v]:= A[v]+1
fi
od:
# alternative program
read("transforms") :
local bdgs, a, x;
a := 0 ;
for bdgs from 1 do
x := n*bdgs ;
# x must have bdgs bits set, so x =bdgs*n >= 2^bdgs-1.
if n < (2^bdgs-1)/x then
break;
elif wt(x) = bdgs then
a := a+1 ;
end if;
end do:
a ;
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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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STATUS
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approved
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