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A375528
a(n) = denominator of Sum_{k = 1..n} 1 / (A000959(k)*A375527(k)).
1
1, 2, 6, 42, 630, 57330, 219172590, 2287458514758690, 523246645674205487113407810300, 34223381526163442974989472671319545640510650941743506071550, 65068880171408068403202506207461768112305307530373013598603234255112994800902512713302330140957468591804616490482800
OFFSET
1,2
COMMENTS
The first few sums S(n) = Sum_{k = 1..n} 1/(A000959(k)*A375527(k)) are: 1/2, 5/6, 41/42, 629/630, 57329/57330,
219172589/219172590, 2287458514758689/2287458514758690,
523246645674205487113407810299/523246645674205487113407810300, ..., and the first 10 or 11 of these sums have the form (c-1)/c, where c is an integer. The present sequence gives the denominators.
For the harmonic series analog, A374663, Rémy Sigrist has shown that all the partial sums have that form (see A374983), and for the prime number analog, A375581, it seems that all partial sums except for n = 4 and 6 have this property (see A375521/A375522).
LINKS
N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 01 2024
STATUS
approved