A081530 a(n) = running sum of the first n harmonic numbers, multiplied by the LCM of 1..n.

1, 5, 26, 77, 522, 669, 5772, 13827, 48610, 55991, 699612, 785633, 11359222, 12530955, 13726712, 29889983, 550271934, 593094837, 12094689300, 12932216325, 13780828710, 14640022575, 356714770680, 376932115005, 1986818142426

Offset

1,2

Comments

Consider triangle in A081525. Write terms in k-th row with denominator = LCM of terms in that row. Sequence gives sum of numerators of terms in n-th row.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = lcm(1..n)*(n+1)*(H(n+1)-1), where H(n) is the n-th harmonic number. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

Equal to A001705(n) / A025527(n). - Martin Fuller, Jan 03 2006

Example

(1), 2*(1 + 3/2), 6*(1 + 3/2 + 11/6), 12*(1 + 3/2 + 11/6 + 25/12).

Maple

H:=n->add(1/i, i=1..n):seq((n+1)*ilcm(seq(j, j=1..n))*(H(n+1)-1), n=1..30); # C. Ronaldo

Mathematica

Table[Sum[HarmonicNumber[k], {k, n}] LCM @@ Range[n], {n, 36}] (* Wouter Meeussen *)

Crossrefs

Cf. A081525, A081526, A081527, A081528, A081529.

Cf. A001705, A025527.

Sequence in context: A048395 A309451 A081886 * A254831 A360350 A145013

Adjacent sequences: A081527 A081528 A081529 * A081531 A081532 A081533

Keyword

nonn

Author

Amarnath Murthy, Mar 27 2003

Extensions

More terms from Wouter Meeussen, Apr 13 2003

Status

approved