A175455 a(n) = H(n) * (lcm(1,2,...,n))^2, where H(n) = harmonic numbers (1/1 + 1/2 + ... + 1/n).

1, 6, 66, 300, 8220, 8820, 457380, 1917720, 17965080, 18600120, 2320468920, 2384502120, 412970037480, 422245703880, 430902992520, 1756076802480, 516336630329520, 524676485052720, 192260441419366320, 194970060218934000, 197550649551855600, 200013939369644400

Offset: 1

Author

Jaroslav Krizek, May 17 2010

Keywords

• nonn

Examples

			For n = 3, a(3) = (1/1 + 1/2 + 1/3) * (1*2*3)^2 = (11/6) * 36 = 66.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000142, A001008, A002805, A003418, A025527, A025529.

Programs

PARI

a(n)={sum(k=1, n, 1/k)*lcm([1..n])^2} \\ Andrew Howroyd, Jan 08 2020

Formula

a(n) = (A001008(n) / A002805(n)) * (A003418(n))^2.

a(n) = A000142(n) * A025529(n) / A025527(n) = A025529(n) * A003418(n).

a(n) = (1/1 + 1/2 + ... + 1/n) * (lcm(1,2,...,n))^2.

Extensions

Terms a(13) and beyond from Andrew Howroyd, Jan 08 2020