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A244583 a(n) = sum of all divisors of all positive integers <= prime(n). 6
4, 8, 21, 41, 99, 141, 238, 297, 431, 690, 794, 1136, 1384, 1524, 1806, 2304, 2846, 3076, 3699, 4137, 4406, 5128, 5645, 6499, 7755, 8401, 8721, 9393, 9783, 10513, 13280, 14095, 15443, 15871, 18232, 18756, 20320, 21873, 22875, 24604, 26274, 27002, 29982, 30684 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Lim_{n->infinity} a(n)/prime(n)^2 = zeta(2)/2 = Pi^2/12 = A072691 = 0.82246703342... For example, at n=2,000,000, the ratio converges to 0.822467033.. (+/-2 in the last digit with increments on n of +100). If the ratio is calculated with a nonprime for the upper summation limit then the ratio runs slightly larger and converges slower. See formula section of A024916 for the general case. - Richard R. Forberg, Jan 04 2015

This is a subsequence of A024916 therefore a(n) also has a symmetric representation. For more information see A236104, A237593. - Omar E. Pol, Jan 05 2015

LINKS

Table of n, a(n) for n=1..44.

FORMULA

a(n) = A024916(A000040(n)).

a(n) = A001248(n) - A050482(n). - Omar E. Pol, Jan 05 2015

MATHEMATICA

a244583[n_] := Sum[DivisorSigma[1, i], {i, #}] & /@ Prime[Range@n]; a244583[44] (* Michael De Vlieger, Jan 06 2015 *)

PROG

(PARI) a(n) = sum(i=1, prime(n), sigma(i)); \\ Michel Marcus, Sep 29 2014

CROSSREFS

Cf. A000040, A000203, A024916, A236104, A237593, A237270, A237271, A244576, A244578.

Sequence in context: A079860 A061256 A180608 * A261031 A077921 A097076

Adjacent sequences:  A244580 A244581 A244582 * A244584 A244585 A244586

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jun 30 2014

EXTENSIONS

More terms from Michel Marcus, Sep 29 2014

STATUS

approved

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Last modified October 20 15:44 EDT 2018. Contains 316389 sequences. (Running on oeis4.)