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A318742 a(n) = Sum_{k=1..n} floor(n/k)^3. 4
1, 9, 29, 74, 136, 254, 382, 596, 833, 1173, 1505, 2057, 2527, 3209, 3921, 4856, 5674, 6928, 7956, 9474, 10882, 12608, 14128, 16506, 18369, 20797, 23141, 26129, 28567, 32259, 35051, 38963, 42483, 46675, 50435, 55904, 59902, 65156, 70092, 76460 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A006218(n) - 3*A024916(n) + 3*A064602(n).

a(n) ~ Zeta(3) * n^3.

MATHEMATICA

Table[Sum[Floor[n/k]^3, {k, 1, n}], {n, 1, 40}]

Accumulate[Table[DivisorSigma[0, k] - 3*DivisorSigma[1, k] + 3*DivisorSigma[2, k], {k, 1, 40}]]

PROG

(PARI) a(n) = sum(k=1, n, (n\k)^3); \\ Michel Marcus, Sep 03 2018

CROSSREFS

Cf. A000005, A000203, A024916, A064602, A064603, A064604.

Cf. A006218, A222548, A318743, A318744.

Sequence in context: A273297 A273268 A273306 * A024922 A193004 A198645

Adjacent sequences:  A318739 A318740 A318741 * A318743 A318744 A318745

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 02 2018

STATUS

approved

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Last modified May 21 15:32 EDT 2019. Contains 323444 sequences. (Running on oeis4.)