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A250130 Numerator of the harmonic mean of the first n primes. 3
2, 12, 90, 840, 11550, 180180, 3573570, 77597520, 2007835830, 64696932300, 2206165391430, 89048857617720, 3955253425853730, 183158658643380420, 9223346738827371150, 521426535635040715680, 32686925952621614864190 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Colin Barker, Table of n, a(n) for n = 1..300

FORMULA

a(n) = n*A002110(n). - L. Edson Jeffery, Jan 04 2015

EXAMPLE

a(3) = 90 because the first 3 primes are [2,3,5] and 3 / (1/2+1/3+1/5) = 90/31.

MAPLE

N:= 100: # to get a(1) to a(N)

B:= ListTools:-PartialSums([seq](1/ithprime(i), i=1..N)):

seq(numer(n/B[n]), n=1..N); # Robert Israel, Nov 13 2014

MATHEMATICA

Table[n/Sum[1/Prime[k], {k, 1, n}], {n, 1, 20}]//Numerator (* Vaclav Kotesovec, Nov 13 2014 *)

Table[n*Product[Prime[j], {j, n}], {n, 17}] (* L. Edson Jeffery, Jan 04 2015 *)

PROG

(PARI)

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

s=vector(30); p=primes(#s); for(k=1, #p, s[k]=numerator( harmonicmean( vector(k, i, p[i])))); s

(PARI) n=0; P=1; forprime(p=2, 100, n++; P *= p; print1(n*P, ", ")) \\ Jeppe Stig Nielsen, Aug 11 2019

CROSSREFS

Cf. A024451 (denominators), A002110 (primorial numbers).

Sequence in context: A121357 A098926 A074610 * A225573 A155639 A103882

Adjacent sequences:  A250127 A250128 A250129 * A250131 A250132 A250133

KEYWORD

nonn

AUTHOR

Colin Barker, Nov 13 2014

STATUS

approved

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Last modified October 21 13:24 EDT 2019. Contains 328299 sequences. (Running on oeis4.)