A081887 Numbers k such that lcm(1..k) equals the denominator of the sum of the first k harmonic numbers.

1, 2, 4, 10, 12, 16, 28, 30, 52, 88, 96, 126, 130, 136, 138, 148, 150, 250, 256, 262, 268, 270, 292, 970, 976, 982, 990, 996, 1008, 1012, 1018, 1020, 1030, 1032, 1038, 1048, 1050, 1060, 1062, 1372, 1380, 1398, 1408, 1422, 1426, 1428, 1432, 1438

Offset

1,2

Comments

k+1 must be a prime, but converse is not true.

Links

Table of n, a(n) for n=1..48.

Example

The sum of the first 4 harmonic numbers is 77/12 and 12 is lcm(1,2,3,4).

Mathematica

big=Table[LCM @@Range[n]/Denominator[ -n+(1+n) HarmonicNumber[n]], {n, 2048}]; Position[big, 1]//Flatten

Prog

(PARI) h(n) = sum(j=1, n, 1/j);
isok(n) = lcm(vector(n, k, k)) == denominator(sum(k=1, n, h(k))); \\ Michel Marcus, Mar 15 2018

Crossrefs

Sequence in context: A129412 A266115 A113536 * A085344 A288225 A047463

Adjacent sequences: A081884 A081885 A081886 * A081888 A081889 A081890

Keyword

nonn

Author

Wouter Meeussen, Apr 13 2003

Extensions

More terms from Wouter Meeussen, Feb 21 2004

Status

approved