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A060436 Numerator of Sum_{k=1..n} d(k)/k, where d() = A000005(). 2
1, 2, 8, 41, 229, 269, 2003, 2213, 2353, 2521, 28571, 30881, 410693, 427853, 443869, 1850551, 31939847, 33301207, 640891093, 664170349, 226316943, 231019823, 5365187609, 16690477147, 84523231511, 85896110711, 784963282799, 802173304199, 23423652688171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The old entry with this sequence number was a duplicate of A054845.

REFERENCES

M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 237.

LINKS

Robert Israel, Table of n, a(n) for n = 1..2296

Vaclav Kotesovec, Graph - The asymptotic ratio of Sum_{k=1..n} d(k)/k

Mathematics.StackExchange, The asymptotic expansion for the weighted sum of divisors, Aug 19 2013.

FORMULA

Sum_{k=1..n} A000005(k)/k = a(n)/A065080(n) ~ log(n)^2/2 + 2*gamma*log(n) + gamma^2 - 2*gamma_1, where gamma is the Euler-Mascheroni constant A001620 and gamma_1 is the first Stieltjes constant A082633. - Vaclav Kotesovec, Aug 30 2018

EXAMPLE

1, 2, 8/3, 41/12, 229/60, 269/60, 2003/420, 2213/420, 2353/420, 2521/420, 28571/4620, 30881/4620, ...

MAPLE

t:= 0:

for n from 1 to 50 do

  t:= t + numtheory:-tau(n)/n;

  A[n]:= numer(t);

od:

seq(A[n], n=1..50); # Robert Israel, Mar 20 2018

MATHEMATICA

l = {}; For[n = 0, n <= 1000, n++, c = 0; If[PrimeQ[n], c = c + 1]; For[k = 1, Prime[k] <= n/2, k++, For[j = 0, Prime[k + j] <= n, j++, If[Sum[Prime[i], {i, k, k + j}] == n, c = c + 1] ] ] AppendTo[l, c] ]; l [From Jake Foster, Oct 27 2008]

CROSSREFS

Cf. A000005, A065080.

Sequence in context: A012534 A092354 A254399 * A020083 A217362 A294084

Adjacent sequences:  A060433 A060434 A060435 * A060437 A060438 A060439

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Nov 02 2008

STATUS

approved

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Last modified March 19 15:02 EDT 2019. Contains 321330 sequences. (Running on oeis4.)