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A071811
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Sum_{k <= 10^n} number of primes (counted with multiplicity) dividing k (A001222).
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0
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0, 15, 239, 2877, 31985, 343614, 3626619, 37861249, 392351272, 4044220058, 41518796555, 424904645958, 4337589196099, 44189168275565, 449411845856902, 4564053529871328, 46294122513328879, 469075734968975581, 4748553675150670580, 47797839092868715542
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OFFSET
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0,2
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COMMENTS
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Also bigomega( (10^n)! ), where bigomega(x): number of prime divisors of x, counted with multiplicity. - Cino Hilliard, Jul 04 2007
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LINKS
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EXAMPLE
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a(1)=15 because bigomega(1) + bigomega(2) + ... + bigomega(10) = 0+1+1+2+1+2+1+3+2+2 = 15.
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MATHEMATICA
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With[{s = Array[PrimeOmega, 10^6]}, {0}~Join~Array[Total@ Take[s, 10^#] &, Floor@ Log10@ Length@ s]] (* Michael De Vlieger, Dec 17 2017 *)
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PROG
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(PARI) s=0; n=0; for(k=1, 10^8, s=s+bigomega(k); if(k==10^n, print1(s, ", "); n++))
(PARI) g(n) = for(x=0, n, print1(bigomega((10^x)!), ", ")) \\ Cino Hilliard, Jul 04 2007
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CROSSREFS
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Cf. A001222 (bigomega), A064182 (corresponding sums for distinct primes).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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