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A024924
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a(n) = sum of prime(k)*floor(n/prime(k)) over k = 1,2,3,...,n.
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3
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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; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = n*A000720(n) - A024934(n). [From Max Alekseyev (maxale(AT)gmail.com), 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)]. [From Max Alekseyev (maxale(AT)gmail.com), Feb 10 2012]
G.f.: Sum(prime(k)*x^prime(k)/(1-x^prime(k)), k=1..infinity)/(1-x). Partial sums of A008472. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 11 2004
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CROSSREFS
| Sequence in context: A161664 A080547 A080555 * A023668 A023564 A173088
Adjacent sequences: A024921 A024922 A024923 * A024925 A024926 A024927
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KEYWORD
| nonn,changed
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| a(0)=0 prepended by Max Alekseyev (maxale(AT)gmail.com), Feb 10 2012
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