A330680 Numbers that begin a run of consecutive integers k such that the denominator of the k-th harmonic number is lcm(1..k).

1, 9, 27, 49, 88, 125, 243, 289, 361, 484, 841, 968, 1164, 1331, 1369, 2401, 3125, 3488, 3721, 6889, 7085, 7761, 7921, 8342, 8502, 9156, 10648, 19683, 22208, 22801, 25886, 28561, 29929, 30877, 32041, 32761, 33178, 36481, 59049, 83521, 87079, 88307, 92199

Offset

1,2

Comments

A098464 lists the numbers k such that lcm(1,2,3,...,k) equals the denominator of the k-th harmonic number H(k) = 1/1 + 1/2 + 1/3 + ... + 1/k.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..308

Example

The numbers k such that the denominator of the k-th harmonic number equals lcm(1..k) begin with the following runs of consecutive integers:
    1,   2,   3,   4,   5;
    9,  10,  11,  12,  13,  14,  15,  16,  17;
   27,  28,  29,  30,  31,  32;
   49,  50,  51,  52,  53;
   88,  89,  90,  91,  92,  93,  94,  95,  96,  97,  98,  99;
  125, 126, 127, ...
so this sequence begins 1, 9, 27, 49, 88, 125, ...

Crossrefs

Cf. A002805 (denominator of H(n)), A003418 (lcm(1..n)), A098464 (numbers k such that A002805(k)=A003418(k)).

Sequence in context: A369564 A020208 A020306 * A069068 A051412 A027468

Adjacent sequences: A330677 A330678 A330679 * A330681 A330682 A330683

Keyword

nonn

Author

Jon E. Schoenfield, Dec 24 2019

Status

approved