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

Author

Jon E. Schoenfield, Dec 24 2019

Keywords

• nonn

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.

Examples

			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, ...
		

Links

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

Crossrefs

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