A250328 Denominator of the harmonic mean of the first n pentagonal numbers.

1, 3, 77, 877, 6271, 36049, 36423, 422137, 49691099, 1448086909, 11631128477, 2334008785, 44471893747, 1827784004699, 832564679309, 39202882860913, 196334425398149, 3473612060358899, 3478128507653999, 205449856947685261, 303604578504856471

Offset: 1

Author

Colin Barker, Nov 18 2014

Keywords

• nonn
• frac
• easy

Comments

a(n+1) is, for n >= 0, also the numerator of the partial sums of the reciprocals of twice the pentagonal numbers {A049450(k+1)}A294513(n)%20(assuming%20that%20A250327(n+1)/(n+1)%20=%20A294513(n)/2).%20-%20_Wolfdieter%20Lang">{k>=0} with the denominators given in A294513(n) (assuming that A250327(n+1)/(n+1) = A294513(n)/2). - _Wolfdieter Lang, Nov 02 2017

Examples

			a(3) = 77 because the pentagonal numbers A000326(n), for n = 1,2,3 are 1, 5, 12 and 3/(1/1+1/5+1/12) = 180/77.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000326, A250327 (numerators).

Programs

Mathematica

With[{s = Array[PolygonalNumber[5, #] &, 21]}, Denominator@ Array[HarmonicMean@ Take[s, #] &, Length@ s]] (* Michael De Vlieger, Nov 02 2017 *)

PARI

harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
s=vector(30); for(k=1, #s, s[k]=denominator(harmonicmean(vector(k, i, (3*i^2-i)/2)))); s