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 A075189 Number of distinct primes in the numerator of the 2^n sums generated from the set 1, 1/2, 1/3, ..., 1/n. 6
 0, 1, 3, 6, 14, 20, 38, 74, 134, 232, 486, 526, 1078, 2036, 2505, 4762, 9929, 14598, 29831, 31521, 52223, 101123, 207892, 215796, 426772, 836665, 1640357, 1689653, 3401483 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Every prime is generated eventually. For the largest generated prime, see A075226. For the smallest odd prime not generated, see A075227. A217712(n) = number of primes occurring exactly once as numerators among the 2^n sums. - Reinhard Zumkeller, Jun 02 2013 LINKS Table of n, a(n) for n=1..29. EXAMPLE a(3) = 3 because 3 sums yield distinct prime numerators: 1+1/2 = 3/2, 1/2+1/3 = 5/6 and 1+1/2+1/3 = 11/6. MATHEMATICA Needs["DiscreteMath`Combinatorica`"]; maxN=20; For[lst={}; prms={}; i=0; n=1, n<=maxN, n++, While[i<2^n-1, i++; s=NthSubset[i, Range[n]]; k=Numerator[Plus@@(1/s)]; If[PrimeQ[k], prms=Union[prms, {k}]]]; AppendTo[lst, Length[prms]]]; lst PROG (Haskell) import Data.Ratio ((%), numerator) import Data.Set (Set, empty, fromList, toList, union, size) a075189 n = a075189_list !! (n-1) a075189_list = f 1 empty empty where f x s s1 = size s1' : f (x + 1) (s `union` fromList hs) s1' where s1' = s1 `union` fromList (filter ((== 1) . a010051') \$ map numerator hs) hs = map (+ 1 % x) \$ 0 : toList s -- Reinhard Zumkeller, May 28 2013 CROSSREFS Cf. A001008, A075135, A075188, A075226, A075227. Cf. A010051. Sequence in context: A175318 A281025 A109757 * A291987 A200823 A093866 Adjacent sequences: A075186 A075187 A075188 * A075190 A075191 A075192 KEYWORD nice,nonn AUTHOR T. D. Noe, Sep 08 2002 EXTENSIONS Terms a(21)-a(29) by Reinhard Zumkeller, May 28 2013 STATUS approved

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Last modified June 19 13:40 EDT 2024. Contains 373503 sequences. (Running on oeis4.)