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A064602 Partial sums of A001157: Sum_{j=1..n} sigma_2(j). 16
1, 6, 16, 37, 63, 113, 163, 248, 339, 469, 591, 801, 971, 1221, 1481, 1822, 2112, 2567, 2929, 3475, 3975, 4585, 5115, 5965, 6616, 7466, 8286, 9336, 10178, 11478, 12440, 13805, 15025, 16475, 17775, 19686, 21056, 22866, 24566, 26776, 28458, 30958 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The subsequence of prime partial sums of A001157 begins: 37, 113, 163, 971, 1481, 112249, 122839, 140729, 145771, 232187, 347731. - Jonathan Vos Post, Feb 11 2010

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Project Euler, Sum of squares of divisors, 2012

FORMULA

a(n) = a(n-1) + A001157(n) = Sum_{j=1..n} sigma_2(j) where sigma_2(j) = A001157(j).

a(n) = Sum_{i=1..n} i^2 * floor(n/i). - Enrique Pérez Herrero, Sep 15 2012

G.f.: (1/(1 - x))*Sum_{k>=1} k^2*x^k/(1 - x^k). - Ilya Gutkovskiy, Jan 02 2017

a(n) ~ Zeta(3) * n^3 / 3. - Vaclav Kotesovec, Sep 02 2018

a(n) = floor((n+1)/2) + Sum_{k=1..floor(n/2)} (1/6) * floor(n/k) * floor(1 + n/k) * (2*floor(n/k) + 1). - Daniel Suteu, Nov 07 2018

MATHEMATICA

Accumulate@ Array[DivisorSigma[2, #] &, 42] (* Michael De Vlieger, Jan 02 2017 *)

PROG

(PARI) a(n) = sum(j=1, n, sigma(j, 2)); \\ Michel Marcus, Dec 15 2013

CROSSREFS

Cf. A001157, A064605.

Cf. A064603, A064604, A248076.

Sequence in context: A048487 A124699 A237601 * A058272 A049712 A092274

Adjacent sequences:  A064599 A064600 A064601 * A064603 A064604 A064605

KEYWORD

nonn

AUTHOR

Labos Elemer, Sep 24 2001

STATUS

approved

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Last modified September 20 22:20 EDT 2019. Contains 327252 sequences. (Running on oeis4.)