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%I #13 Sep 14 2020 16:43:06
%S 1,3,11,5,137,7,3,11,761,7129,11,61,97,863,13,509,29,43,919,1049,1117,
%T 29,41233,17,8431,37,1138979,19,39541,37,7440427,5,11167027,18858053,
%U 3,23,53,227,761,583859,5,577,467183,109,312408463
%N Table, read by rows: row n contains the prime divisors of A001008 (numerator of n-th harmonic number), without repetitions.
%C Row 1 is taken to be {1} instead of being empty, by convention.
%e n | A001008(n) written as product of primes
%e -----+---------------------------------------------
%e 1 | 1 (empty product)
%e 2 | 3
%e 3 | 11
%e 4 | 5 * 5 (So 5 is the only prime divisor, and row(4) = {5}.)
%e 5 | 137
%e 6 | 7 * 7
%e 7 | 3 * 11 * 11 whence row(7) = {3, 11}.)
%e 8 | 761
%e 9 | 7129
%e 10 | 11 * 11 * 61 whence row(10) = {11, 61}.
%e 11 | 97 * 863
%e 12 | 13 * 13 * 509 whence row(16) = {13, 509}.
%e 13 | 29 * 43 * 919 whence row(13) = {29, 43, 919}.
%e 14 | 1049 * 1117
%e 15 | 29 * 41233
%e 16 | 17 * 17 * 8431 whence row(16) = {17, 8431}.
%e 17 | 37 * 1138979
%e 18 | 19 * 19 * 39541 whence row(18) = {19, 39541}.
%e 19 | 37 * 7440427
%e 20 | 5 * 11167027
%e etc.
%t Table[FactorInteger[Numerator[HarmonicNumber[n]]][[All,1]],{n,30}]// Flatten (* _Harvey P. Dale_, Sep 14 2020 *)
%o (PARI) row(n)={if(n>1, factor(A001008(n))[,1]~, [1])}
%Y Cf. A001008.
%Y Cf. A308967 (number of prime factors), A308968 (table of factorization), A308970 & A308971 (smallest & greatest prime factor) of A001008(n).
%K nonn,tabf
%O 1,2
%A _M. F. Hasler_, Jul 03 2019
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