A071811 a(n) = Sum_{k = 1..10^n} number of primes (counted with multiplicity) dividing k (A001222).
0, 15, 239, 2877, 31985, 343614, 3626619, 37861249, 392351272, 4044220058, 41518796555, 424904645958, 4337589196099, 44189168275565, 449411845856902, 4564053529871328, 46294122513328879, 469075734968975581, 4748553675150670580, 47797839092868715542
Offset: 0
Keywords
Examples
a(1) = 15 because bigomega(1) + bigomega(2) + ... + bigomega(10) = 0+1+1+2+1+2+1+3+2+2 = 15.
Crossrefs
Programs
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Mathematica
With[{s = Array[PrimeOmega, 10^6]}, {0}~Join~Array[Total@ Take[s, 10^#] &, Floor@ Log10@ Length@ s]] (* Michael De Vlieger, Dec 17 2017 *) -
PARI
s=0; n=0; for(k=1,10^8, s=s+bigomega(k); if(k==10^n,print1(s,","); n++))
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PARI
g(n) = for(x=0,n,print1(bigomega((10^x)!),",")) \\ Cino Hilliard, Jul 04 2007
Formula
From Amiram Eldar, Oct 11 2024: (Start)
a(n) = A022559(10^n).
a(n) ~ 10^n * (log(log(10^n)) + B_2), where B_2 = A083342. (End)
Extensions
a(9) from Charles R Greathouse IV, Dec 11 2008
a(11)-a(12) from Giovanni Resta, Oct 26 2012
a(13)-a(17) from Hiroaki Yamanouchi, Aug 28 2014
a(18)-a(19) from Henri Lifchitz, Dec 17 2017
Comments