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A338120 a(n) is the least index k such that the n-th odd squarefree number A056911(n) divides A110566(k). 0
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 (list; graph; refs; listen; history; text; internal format)
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: A097811 A328366 A143711 * A077539 A002943 A068377

Adjacent sequences:  A338117 A338118 A338119 * A338121 A338122 A338123

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Jan 29 2021

STATUS

approved

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Last modified October 19 03:10 EDT 2021. Contains 348073 sequences. (Running on oeis4.)