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