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A250130
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Numerator of the harmonic mean of the first n primes.
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4
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2, 12, 90, 840, 11550, 180180, 3573570, 77597520, 2007835830, 64696932300, 2206165391430, 89048857617720, 3955253425853730, 183158658643380420, 9223346738827371150, 521426535635040715680, 32686925952621614864190, 2111190864469325477698860
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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a(3) = 90 because the first 3 primes are [2,3,5] and 3 / (1/2+1/3+1/5) = 90/31.
The first fractions are 2/1, 12/5, 90/31, 840/247, 11550/2927, 180180/40361, 3573570/716167, 77597520/14117683, ...
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MAPLE
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N:= 100: # to get a(1) to a(N)
B:= ListTools:-PartialSums([seq](1/ithprime(i), i=1..N)):
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MATHEMATICA
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Table[n/Sum[1/Prime[k], {k, 1, n}], {n, 1, 20}]//Numerator (* Vaclav Kotesovec, Nov 13 2014 *)
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PROG
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(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
(Python)
from sympy import prime
from fractions import Fraction
def a(n):
return (n/sum(Fraction(1, prime(k)) for k in range(1, n+1))).numerator
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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