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A024924 a(n) = sum of prime(k)*floor(n/prime(k)) over k = 1,2,3,...,n. 8
0, 0, 2, 5, 7, 12, 17, 24, 26, 29, 36, 47, 52, 65, 74, 82, 84, 101, 106, 125, 132, 142, 155, 178, 183, 188, 203, 206, 215, 244, 254, 285, 287, 301, 320, 332, 337, 374, 395, 411, 418, 459, 471, 514, 527, 535, 560, 607, 612, 619, 626, 646, 661, 714, 719, 735, 744, 766, 797, 856 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n > 2, sum of all distinct prime factors composing numbers from 2 to n.

LINKS

Table of n, a(n) for n=0..59.

FORMULA

a(n) = n*A000720(n) - A024934(n). - Max Alekseyev, Feb 10 2012

a(n) = A034387([n/1]) + A034387([n/2]) + ... + A034387([n/n]). Terms can be computed efficiently with the following formula: a(n) = A034387([n/1]) + ... + A034387([n/m]) - m*A034387([n/m]) + Sum_{prime p<=n/m} p*[n/p], where m = [sqrt(n)]. - Max Alekseyev, Feb 10 2012

G.f.: Sum_{k >=1} (prime(k)*x^prime(k)/(1-x^prime(k)))/(1-x). - Vladeta Jovovic, Aug 11 2004

PROG

(PARI) a(n) = sum(k=1, n, prime(k)*(n\prime(k))); \\ Michel Marcus, Mar 01 2015

CROSSREFS

Partial sums of A008472. - Vladeta Jovovic, Aug 11 2004

Cf. A000720, A008472, A024934, A034387.

Sequence in context: A161664 A080547 A080555 * A023668 A023564 A173088

Adjacent sequences:  A024921 A024922 A024923 * A024925 A024926 A024927

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

a(0)=0 prepended by Max Alekseyev, Feb 10 2012

STATUS

approved

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Last modified September 25 22:57 EDT 2018. Contains 315425 sequences. (Running on oeis4.)