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A330680 Numbers that begin a run of consecutive integers k such that the denominator of the k-th harmonic number is lcm(1..k). 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..43.

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: A133636 A020208 A020306 * A069068 A051412 A027468

Adjacent sequences:  A330677 A330678 A330679 * A330681 A330682 A330683

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Dec 24 2019

STATUS

approved

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Last modified May 29 02:05 EDT 2020. Contains 334690 sequences. (Running on oeis4.)