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 A072207 a(0) = 1; for n>0, a(n) = number of distinct sums of subsets of {1, 1/2, 1/3, 1/4, ..., 1/n} (allowing the empty subset). 4
 1, 2, 4, 8, 16, 32, 52, 104, 208, 416, 832, 1664, 1856, 3712, 7424, 9664, 19328, 38656, 59264, 118528, 126976, 224128, 448256, 896512, 936832, 1873664, 3747328, 7494656, 7771136, 15542272, 15886336, 31772672, 63545344, 112064512, 224129024, 231010304, 237031424, 474062848, 948125696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Define L to be a set of rational numbers with L={0}, s=1 in generation 0 and the rule "replace each term t in L with terms t-1/s, t+1/s, then increment s" to generate the next generation. a(n) is the size of the set in generation n. First generation = {-1,1}, second generation = {-3/2,-1/2,1/2,3/2}, 3rd generation = {-11/6,-7/6,-5/6,-1/6,1/6,5/6,7/6,11/6}. - Dylan Hamilton, Oct 28 2010 If n is a prime power, a(n) = 2*a(n-1). However, this is not "if and only if", e.g., a(10) = 2*a(9). - Robert Israel, Nov 23 2016 LINKS M. N. Bleicher and P. ErdÅ‘s, The number of distinct subsums of sum 1..N 1/i, Math. Comp. 29 (1975), 29-42, Collection of articles dedicated to Derrick Henry Lehmer on the occasion of his seventieth birthday, see Front matter. FORMULA a(p) = 2 * a(p-1) for p prime. a(2*p) = 2 * a(2*p-1) for p>3 prime. - Giovanni Resta, Jul 18 2019 MAPLE S[1]:= {0, 1}: A[1]:= 2: for n from 2 to 30 do   S[n]:= S[n-1] union (1/n +~ S[n-1]);   A[n]:= nops(S[n]); od: seq(A[i], i=1..30); # Robert Israel, Nov 23 2016 MATHEMATICA w = {0}; o = {1}; s = 1 Do[w = Union[Flatten[{w - (1/s), w + (1/s)}]]; AppendTo[o, Length[w]]; ++s, {NumberOfApplications}]; o # Dylan Hamilton, Oct 28 2010 CROSSREFS Cf. A175952. Sequence in context: A306314 A007055 A175951 * A176718 A033860 A231388 Adjacent sequences:  A072204 A072205 A072206 * A072208 A072209 A072210 KEYWORD nonn AUTHOR John W. Layman, Jul 03 2002 EXTENSIONS More terms from Vladeta Jovovic, Jul 05 2002 Terms through a(32) from Sean A. Irvine, Nov 29 2010 Merged A175951 with this entry at the suggestion of Robert Israel. - N. J. A. Sloane, Nov 24 2016 Offset set to 0 and a(33)-a(38) from Giovanni Resta, Jul 20 2019 STATUS approved

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Last modified June 20 18:42 EDT 2021. Contains 345199 sequences. (Running on oeis4.)