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A143127
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Sum of k*d(k) over k=1,2,...,n, where d(k) is the number of divisors of k.
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3
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1, 5, 11, 23, 33, 57, 71, 103, 130, 170, 192, 264, 290, 346, 406, 486, 520, 628, 666, 786, 870, 958, 1004, 1196, 1271, 1375, 1483, 1651, 1709, 1949, 2011, 2203, 2335, 2471, 2611, 2935, 3009, 3161, 3317, 3637, 3719, 4055, 4141, 4405, 4675, 4859, 4953, 5433
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n) = sum_{k=1..n} k*d(k) = sum_{k=1..n} A038040(k)
a(n) = sum_{m=1..floor(sqrt(n))} m*(m+floor(n/m))*(floor(n/m)+1-m) - A000330(floor(sqrt(n))) = 2*A083356(n) - A000330(floor(sqrt(n))). [From Max Alekseyev]
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EXAMPLE
| a(3) = 11 = (1 + 4 + 6), where n*d(n) = (1, 4, 6, 12, 10, 24,...).
a(4) = 23 = (8 + 7 + 5 + 3), where (8, 7, 5, 3) = row 4 of triangle A110661.
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CROSSREFS
| Cf. A000005, A038040, A083356.
Row sums of triangle A110661.
Row sums of triangle A143310 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 06 2008]
Sequence in context: A152533 A161896 A167610 * A061769 A169744 A190148
Adjacent sequences: A143124 A143125 A143126 * A143128 A143129 A143130
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 26 2008
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EXTENSIONS
| More terms from Carl Najafi (carlnajafi(AT)gmail.com), Dec 24 2011
Edited by Max Alekseyev (maxale(AT)gmail.com), Jan 31 2012
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