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

Author

Alexander Adamchuk, Jul 07 2006

Keywords

• frac
• nonn

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.

Crossrefs

Cf. A061002, A001008.

Programs

Mathematica

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

Formula

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