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A308968 Table, read by rows: row n contains the prime factors of A001008(n) (numerator of n-th harmonic number), with multiplicity.

%I A308968 #14 Oct 30 2019 13:24:41
%S A308968 1,3,11,5,5,137,7,7,3,11,11,761,7129,11,11,61,97,863,13,13,509,29,43,
%T A308968 919,1049,1117,29,41233,17,17,8431,37,1138979,19,19,39541,37,7440427,
%U A308968 5,11167027,18858053,3,23,23,53,227,761,583859,5,577,467183,109,312408463
%N A308968 Table, read by rows: row n contains the prime factors of A001008(n) (numerator of n-th harmonic number), with multiplicity.
%C A308968 Row 1 is taken to be {1} instead of being empty, by convention.
%C A308968 Length, first = smallest and last = largest term of the rows are given in A308967, A308970 and A308971, respectively. See A308969 for prime divisors without repetition.
%H A308968 M. F. Hasler, <a href="/A308968/a308968.txt">Rows 1 through 170</a>.
%e A308968    n | A001008(n) written as product of primes
%e A308968 -----+---------------------------------------------
%e A308968    1 | 1 (empty product)
%e A308968    2 | 3
%e A308968    3 | 11
%e A308968    4 | 5 * 5
%e A308968    5 | 137
%e A308968    6 | 7 * 7
%e A308968    7 | 3 * 11 * 11
%e A308968    8 | 761
%e A308968    9 | 7129
%e A308968   10 | 11 * 11 * 61
%e A308968   11 | 97 * 863
%e A308968   12 | 13 * 13 * 509
%e A308968   13 | 29 * 43 * 919
%e A308968   14 | 1049 * 1117
%e A308968   15 | 29 * 41233
%e A308968   16 | 17 * 17 * 8431
%e A308968   17 | 37 * 1138979
%e A308968   18 | 19 * 19 * 39541
%e A308968   19 | 37 * 7440427
%e A308968   20 | 5 * 11167027
%e A308968 etc.
%o A308968 (PARI) A308968_row(n)={if(n>1, concat(apply(f->vector(f[2],i,f[1]), Col(factor(A001008(n)))~)),[1])}
%Y A308968 Cf. A001008, A308967 (row lengths, for n > 1).
%Y A308968 Cf. A308969 (prime divisors without repetition), A308970 (column 1 = first / smallest term of each row), A308971 (last / greatest term in each row).
%K A308968 nonn,tabf
%O A308968 1,2
%A A308968 _M. F. Hasler_, Jul 03 2019