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 A065413 Number of positive solutions to "numbers that are n times their number of binary 1's". 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,23 COMMENTS Equivalently, this is the number of ways to write n as an arithmetic mean of distinct powers of 2. [Brian Kell, Mar 01 2009] LINKS Peter Kagey, Table of n, a(n) for n = 1..10000 EXAMPLE 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. 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 CROSSREFS Cf. A000120, A037478, A058898, A272797 (greedy inverse). Sequence in context: A229038 A229143 A330018 * A107131 A027200 A035654 Adjacent sequences: A065410 A065411 A065412 * A065414 A065415 A065416 KEYWORD base,nonn AUTHOR Henry Bottomley, Nov 23 2001 STATUS approved

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Last modified December 6 16:00 EST 2022. Contains 358644 sequences. (Running on oeis4.)