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A308969
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Table, read by rows: row n contains the prime divisors of A001008 (numerator of n-th harmonic number), without repetitions.
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4
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1, 3, 11, 5, 137, 7, 3, 11, 761, 7129, 11, 61, 97, 863, 13, 509, 29, 43, 919, 1049, 1117, 29, 41233, 17, 8431, 37, 1138979, 19, 39541, 37, 7440427, 5, 11167027, 18858053, 3, 23, 53, 227, 761, 583859, 5, 577, 467183, 109, 312408463
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OFFSET
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1,2
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COMMENTS
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Row 1 is taken to be {1} instead of being empty, by convention.
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LINKS
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EXAMPLE
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n | A001008(n) written as product of primes
-----+---------------------------------------------
1 | 1 (empty product)
2 | 3
3 | 11
4 | 5 * 5 (So 5 is the only prime divisor, and row(4) = {5}.)
5 | 137
6 | 7 * 7
7 | 3 * 11 * 11 whence row(7) = {3, 11}.)
8 | 761
9 | 7129
10 | 11 * 11 * 61 whence row(10) = {11, 61}.
11 | 97 * 863
12 | 13 * 13 * 509 whence row(16) = {13, 509}.
13 | 29 * 43 * 919 whence row(13) = {29, 43, 919}.
14 | 1049 * 1117
15 | 29 * 41233
16 | 17 * 17 * 8431 whence row(16) = {17, 8431}.
17 | 37 * 1138979
18 | 19 * 19 * 39541 whence row(18) = {19, 39541}.
19 | 37 * 7440427
20 | 5 * 11167027
etc.
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MATHEMATICA
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Table[FactorInteger[Numerator[HarmonicNumber[n]]][[All, 1]], {n, 30}]// Flatten (* Harvey P. Dale, Sep 14 2020 *)
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PROG
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(PARI) row(n)={if(n>1, factor(A001008(n))[, 1]~, [1])}
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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