A120284 Numerator of absolute value of Sum_{k=1..n} (-1)^(k+1)*(2*k+1)*(Sum_{i=1..k} 1/i).

3, 9, 25, 125, 147, 343, 761, 6849, 7381, 81191, 86021, 1118273, 1171733, 1171733, 2436559, 41421503, 42822903, 271211719, 279175675, 55835135, 19093197, 439143531, 1347822955, 33695573875, 34395742267, 309561680403, 315404588903

Offset

1,1

Comments

p^3 divides a(p-1) for prime p>3, a(p-1)/p^3=A061002[n], a(p-1)/p=A001008(p-1) for p>2. p^2 divides a(p-2) for prime p>3. p^3 divides a(p^2-1) for prime p>3. p divides a(p^2-2) for prime p>3. p^3 divides a(p^3-1) for prime p>3. p^3 divides a(p^4-1) for prime p>3.

Links

Table of n, a(n) for n=1..27.

Formula

a(n) = numerator(abs(Sum_{k=1..n} (-1)^(k+1)*(2*k+1)*(Sum_{i=1..k} 1/i))).

Mathematica

Numerator[Abs[Table[Sum[(-1)^(k+1)*(2k+1)*Sum[1/i, {i, 1, k}], {k, 1, n}], {n, 1, 30}]]]

Crossrefs

Cf. A061002, A001008.

Sequence in context: A012771 A351891 A178061 * A074440 A006204 A013572

Adjacent sequences: A120281 A120282 A120283 * A120285 A120286 A120287

Keyword

frac,nonn

Author

Alexander Adamchuk, Jul 07 2006

Status

approved