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A250551 Denominator of the harmonic mean of the first n positive 10-gonal numbers. 5
1, 11, 307, 8117, 139393, 982381, 4935773, 287319059, 1056494083, 39179109811, 1609331378051, 4835480422963, 33892787092141, 1798339013862173, 34201770221163407, 4176177999344899729, 4179324192635626369, 32062945622467289429, 2341997846273161559117 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n+1) is, for n >= 0, also the numerator of the partial sums of the reciprocal of the positive decagonal numbers A001107(n+1) with the denominators A294515(n) (provided A294515(n) = A250550(n+1)/(n+1)). - Wolfdieter Lang, Nov 02 2017

LINKS

Colin Barker, Table of n, a(n) for n = 1..850

FORMULA

a(n) = denominator(r(n)) with the rationals r(n) = n/Sum_{k=1..n} A001107(n), n >= 1. See the name. - Wolfdieter Lang, Nov 02 2017

EXAMPLE

a(3) = 307 because the first 3 positive decagonal numbers A001107 are [1,10,27], and 3/(1/1+1/10+1/27) = 810/307.

MATHEMATICA

With[{s = Array[PolygonalNumber[10, #] &, 19]}, Denominator@ Array[HarmonicMean@ Take[s, #] &, Length@ s]] (* Michael De Vlieger, Nov 02 2017 *)

PROG

(PARI)

harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])

s=vector(30); for(n=1, #s, s[n]=denominator(harmonicmean(vector(n, k, (8*k^2-6*k)/2)))); s

CROSSREFS

Cf. A001107 (10-gonal numbers), A250550 (numerators).

Sequence in context: A012079 A180056 A172506 * A001280 A100445 A193890

Adjacent sequences:  A250548 A250549 A250550 * A250552 A250553 A250554

KEYWORD

nonn,frac,easy

AUTHOR

Colin Barker, Nov 25 2014

STATUS

approved

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Last modified October 23 11:41 EDT 2021. Contains 348212 sequences. (Running on oeis4.)