login
A081887
Numbers k such that lcm(1..k) equals the denominator of the sum of the first k harmonic numbers.
0
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.
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
KEYWORD
nonn
AUTHOR
Wouter Meeussen, Apr 13 2003
EXTENSIONS
More terms from Wouter Meeussen, Feb 21 2004
STATUS
approved