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A175254 a(n) = Sum_{k<=n} A000203(k) * (n-k+1), where A000203(m) = sum of divisors of m. 16
1, 5, 13, 28, 49, 82, 123, 179, 248, 335, 434, 561, 702, 867, 1056, 1276, 1514, 1791, 2088, 2427, 2798, 3205, 3636, 4127, 4649, 5213, 5817, 6477, 7167, 7929, 8723, 9580, 10485, 11444, 12451, 13549, 14685, 15881, 17133, 18475, 19859, 21339, 22863, 24471, 26157 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial sums of A024916. - Omar E. Pol, Jul 03 2014

a(n) is also the volume of the irregular pyramid with n steps described in A245092. - Omar E. Pol, Aug 12 2015

Also the alternating row sums of A262612. - Omar E. Pol, Nov 23 2015

LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..2209

FORMULA

Conjecture: a(n) = Sum_{k=0..n} A006218(n-k). - R. J. Mathar, Oct 17 2012

a(n) = A000330(n) - A072481(n). - Omar E. Pol, Aug 12 2015

a(n) ~ Pi^2*n^3/36. - Vaclav Kotesovec, Sep 25 2016

G.f.: (1/(1 - x)^2)*Sum_{k>=1} k*x^k/(1 - x^k). - Ilya Gutkovskiy, Jan 03 2017

a(n) = Sum_{k=1..n} Sum_{i=1..k} k - (k mod i). - Wesley Ivan Hurt, Sep 13 2017

EXAMPLE

For n = 4: a(4) = sigma(1)*4 + sigma(2)*3 + sigma(3)*2 + sigma(4)*1 = 1*4 + 3*3 + 4*2 + 7*1 = 28.

MATHEMATICA

Table[Sum[DivisorSigma[1, k] (n - k + 1), {k, n}], {n, 45}] (* Michael De Vlieger, Nov 24 2015 *)

PROG

(PARI) a(n) = sum(x=1, n, sigma(x)*(n-x+1)) \\ Michel Marcus, Mar 18 2013

CROSSREFS

Cf. A000203, A006218, A024916, A072481, A245092, A262612.

Sequence in context: A272045 A248860 A185039 * A211636 A055328 A027962

Adjacent sequences:  A175251 A175252 A175253 * A175255 A175256 A175257

KEYWORD

nonn,easy,changed

AUTHOR

Jaroslav Krizek, Mar 14 2010

EXTENSIONS

Corrected by Jaroslav Krizek, Mar 17 2010

More terms by Michel Marcus, Mar 18 2013

STATUS

approved

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Last modified September 26 03:18 EDT 2017. Contains 292502 sequences.