A250551 - OEIS

%I #14 Nov 06 2017 04:58:36

%S 1,11,307,8117,139393,982381,4935773,287319059,1056494083,39179109811,

%T 1609331378051,4835480422963,33892787092141,1798339013862173,

%U 34201770221163407,4176177999344899729,4179324192635626369,32062945622467289429,2341997846273161559117

%N Denominator of the harmonic mean of the first n positive 10-gonal numbers.

%C 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

%H Colin Barker, <a href="/A250551/b250551.txt">Table of n, a(n) for n = 1..850</a>

%F 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

%e 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.

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

%o (PARI)

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

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

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

%K nonn,frac,easy

%O 1,2

%A _Colin Barker_, Nov 25 2014