A065413 Number of positive solutions to "numbers that are n times their number of binary 1's".
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
Offset: 1
Examples
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.
Links
- Peter Kagey, Table of n, a(n) for n = 1..10000
Programs
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Maple
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: seq(A[i],i=1..N); # Robert Israel, May 06 2016 # alternative program read("transforms") : A065413 := proc(n) 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 ; end proc: # R. J. Mathar, May 11 2016
Comments