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A318743 a(n) = Sum_{k=1..n} floor(n/k)^4. 4
1, 17, 83, 274, 644, 1396, 2502, 4388, 6919, 10743, 15385, 22407, 30233, 41209, 53853, 70650, 88636, 113308, 138654, 172332, 207984, 252416, 298002, 358654, 417873, 492065, 569061, 663427, 756053, 875541, 989063, 1130915, 1272967, 1441383, 1607147, 1817080 (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) + 4*A024916(n) - 6*A064602(n) + 4*A064603(n).

a(n) ~ Zeta(4) * n^4.

a(n) ~ Pi^4 * n^4 / 90.

MATHEMATICA

Table[Sum[Floor[n/k]^4, {k, 1, n}], {n, 1, 40}]

Accumulate[Table[-DivisorSigma[0, k] + 4*DivisorSigma[1, k] - 6*DivisorSigma[2, k] + 4*DivisorSigma[3, k], {k, 1, 40}]]

PROG

(PARI) a(n) = sum(k=1, n, (n\k)^4); \\ Michel Marcus, Sep 03 2018

CROSSREFS

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

Cf. A006218, A222548, A318742, A318744.

Sequence in context: A296401 A259142 A142059 * A193046 A158528 A197346

Adjacent sequences:  A318740 A318741 A318742 * A318744 A318745 A318746

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 02 2018

STATUS

approved

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Last modified June 19 13:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)