A338120 a(n) is the least index k such that the n-th odd squarefree number A056911(n) divides A110566(k).

1, 6, 20, 42, 33, 156, 20, 272, 342, 2058, 506, 377, 930, 77, 14406, 629, 162, 1640, 559, 2162, 4624, 1166, 110, 6498, 3422, 610, 342732, 4422, 506, 4970, 5256, 42, 6162, 6806

Offset

1,2

Comments

According to a theorem proven by Shiu (2016), a(n) exists for all n.

Links

Table of n, a(n) for n=1..34.

Peter Shiu, The denominators of harmonic numbers, arXiv:1607.02863 [math.NT], 2016.

Example

   n  A056911(n)  a(n) = k          A110566(k)
  --  ----------  --------  --------------------------
   1       1            1            1 =  1 * 1
   2       3            6            3 =  3 * 1
   3       5           20           15 =  5 * 3
   4       7           42           77 =  7 * 11
   5      11           33           11 = 11 * 1
   6      13          156           13 = 13 * 1
   7      15           20           15 = 15 * 1
   8      17          272           17 = 17 * 1
   9      19          342          931 = 19 * 49
  10      21         2058         1911 = 21 * 91
  11      23          506         1725 = 23 * 75
  12      29          377          319 = 29 * 11
  13      31          930         3751 = 31 * 121
  14      33           77           33 = 33 * 1
  15      35        14406   2430488445 = 35 * 69442527
  16      37          629        20313 = 37 * 549
  17      39          162           39 = 39 * 1
  18      41         1640         6519 = 41 * 159
  19      43          559          645 = 43 * 15
  20      47         2162        12831 = 47 * 273
  21      51         4624         9537 = 51 * 187
  22      53         1166           53 = 53 * 1
  23      55          110           55 = 55 * 1
  24      57         6498    419498967 = 57 * 7359631
  25      59         3422         6431 = 59 * 109
  26      61          610        41175 = 61 * 675
  27      65       342732       974285 = 65 * 14989
  28      67         4422         2211 = 67 * 33
  29      69          506         1725 = 69 * 25
  30      71         4970         2343 = 71 * 33
  31      73         5256         7227 = 73 * 99
  32      77           42           77 = 77 * 1
  33      79         6162     91801713 = 79 * 1162047
  34      83         6806      1200097 = 83 * 14459

Mathematica

max = 64; osf = Select[Range[1, 64, 2], SquareFreeQ]; m = Length[osf]; c = 0; s = Table[0, {m}]; h = 0; lcm = 1; n = 1; While[c < m, h += 1/n; lcm = LCM[lcm, n];  r = lcm/Denominator[h]; Do[If[s[[k]] == 0 && Divisible[r, osf[[k]]], c++; s[[k]] = n], {k, 1, m}]; n++]; s

Crossrefs

Cf. A002805, A003418, A110566, A056911, A112822.

Sequence in context: A328366 A369348 A143711 * A077539 A068377 A002943

Adjacent sequences: A338117 A338118 A338119 * A338121 A338122 A338123

Keyword

nonn,more

Author

Amiram Eldar, Jan 29 2021

Status

approved