A187487 Numerator of n minus n-th harmonic number.

0, 1, 7, 23, 163, 71, 617, 1479, 15551, 17819, 221209, 246619, 3538687, 3873307, 4209643, 9094961, 166145857, 59239139, 1199057081, 254554945, 89778475, 94716499, 2292289173, 7218943253, 189040347533

Offset: 1

Author

Alonso del Arte, Mar 10 2011

Keywords

• nonn
• frac
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..2286

Crossrefs

Denominators are in A002805.

Cf. A001008 (numerators of the harmonic numbers). Adding this sequence to that sequence gives A102928.

Programs

Maple

f:=n -> numer(n - harmonic(n)):map(f, [$1..100]); # Robert Israel, Apr 26 2021

Mathematica

Numerator[Table[n - HarmonicNumber[n], {n, 25}]]

PARI

a(n) = numerator(n - sum(i=1, n, 1/i)); \\ Michel Marcus, Apr 26 2021

Formula

a(n) = n - Sum_{i = 1..n} 1/i.

a(n) = Sum_{i = 2..n} (i - 1)/i.