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A075188 Number of times that the numerator of a sum generated from the set 1, 1/2, 1/3,..., 1/n is prime. +0
4
0, 1, 3, 9, 19, 43, 79, 162, 307, 607, 1075, 2186, 3872, 7573, 15101, 29139, 52295, 104953, 189915, 379275 (list; graph; listen)
OFFSET

1,3

COMMENT

Note that for each n there are only 2^(n-1) new sums to consider. Surprisingly, nearly half of the sums have a prime numerator. For the number of unique primes, see A075189. For the largest generated prime, see A075226. For the smallest odd prime not generated, see A075227.

EXAMPLE

a(3) = 3 because 3 sums yield 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[cnt=0; lst={}; 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], cnt++ ]]; AppendTo[lst, cnt]]; lst

CROSSREFS

Cf. A001008, A075135, A075189, A075226, A075227.

Sequence in context: A145947 A153084 A147371 this_sequence A051894 A146393 A147431

Adjacent sequences: A075185 A075186 A075187 this_sequence A075189 A075190 A075191

KEYWORD

nice,nonn

AUTHOR

T. D. Noe (noe(AT)sspectra.com), Sep 08 2002

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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