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A308969 Table, read by rows: row n contains the prime divisors of A001008 (numerator of n-th harmonic number), without repetitions.

%I A308969 #16 Dec 09 2024 17:27:59
%S A308969 1,3,11,5,137,7,3,11,761,7129,11,61,97,863,13,509,29,43,919,1049,1117,
%T A308969 29,41233,17,8431,37,1138979,19,39541,37,7440427,5,11167027,18858053,
%U A308969 3,23,53,227,761,583859,5,577,467183,109,312408463
%N A308969 Table, read by rows: row n contains the prime divisors of A001008 (numerator of n-th harmonic number), without repetitions.
%C A308969 Row 1 is taken to be {1} instead of being empty, by convention.
%e A308969    n | A001008(n) written as product of primes
%e A308969 -----+---------------------------------------------
%e A308969    1 | 1 (empty product)
%e A308969    2 | 3
%e A308969    3 | 11
%e A308969    4 | 5 * 5   (So 5 is the only prime divisor, and row(4) = {5}.)
%e A308969    5 | 137
%e A308969    6 | 7 * 7
%e A308969    7 | 3 * 11 * 11       whence row(7) = {3, 11}.
%e A308969    8 | 761
%e A308969    9 | 7129
%e A308969   10 | 11 * 11 * 61      whence row(10) = {11, 61}.
%e A308969   11 | 97 * 863
%e A308969   12 | 13 * 13 * 509     whence row(16) = {13, 509}.
%e A308969   13 | 29 * 43 * 919     whence row(13) = {29, 43, 919}.
%e A308969   14 | 1049 * 1117
%e A308969   15 | 29 * 41233
%e A308969   16 | 17 * 17 * 8431    whence row(16) = {17, 8431}.
%e A308969   17 | 37 * 1138979
%e A308969   18 | 19 * 19 * 39541   whence row(18) = {19, 39541}.
%e A308969   19 | 37 * 7440427
%e A308969   20 | 5 * 11167027
%e A308969 etc.
%t A308969 Table[FactorInteger[Numerator[HarmonicNumber[n]]][[All,1]],{n,30}]// Flatten (* _Harvey P. Dale_, Sep 14 2020 *)
%o A308969 (PARI) row(n)={if(n>1, factor(A001008(n))[,1]~, [1])}
%Y A308969 Cf. A001008.
%Y A308969 Cf. A308967 (number of prime factors), A308968 (table of factorization), A308970 & A308971 (smallest & greatest prime factor) of A001008(n).
%K A308969 nonn,tabf
%O A308969 1,2
%A A308969 _M. F. Hasler_, Jul 03 2019