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

1,3

Links

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

Formula

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

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

Denominators are in A002805.

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

Sequence in context: A158954 A056205 A099051 * A299643 A034192 A050918

Adjacent sequences: A187484 A187485 A187486 * A187488 A187489 A187490

Keyword

nonn,frac,easy

Author

Alonso del Arte, Mar 10 2011

Status

approved