A308968 - OEIS

%I #14 Oct 30 2019 13:24:41

%S 1,3,11,5,5,137,7,7,3,11,11,761,7129,11,11,61,97,863,13,13,509,29,43,

%T 919,1049,1117,29,41233,17,17,8431,37,1138979,19,19,39541,37,7440427,

%U 5,11167027,18858053,3,23,23,53,227,761,583859,5,577,467183,109,312408463

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

%C Row 1 is taken to be {1} instead of being empty, by convention.

%C 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 M. F. Hasler, <a href="/A308968/a308968.txt">Rows 1 through 170</a>.

%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

%e    5 | 137

%e    6 | 7 * 7

%e    7 | 3 * 11 * 11

%e    8 | 761

%e    9 | 7129

%e   10 | 11 * 11 * 61

%e   11 | 97 * 863

%e   12 | 13 * 13 * 509

%e   13 | 29 * 43 * 919

%e   14 | 1049 * 1117

%e   15 | 29 * 41233

%e   16 | 17 * 17 * 8431

%e   17 | 37 * 1138979

%e   18 | 19 * 19 * 39541

%e   19 | 37 * 7440427

%e   20 | 5 * 11167027

%e etc.

%o (PARI) A308968_row(n)={if(n>1, concat(apply(f->vector(f[2],i,f[1]), Col(factor(A001008(n)))~)),[1])}

%Y Cf. A001008, A308967 (row lengths, for n > 1).

%Y Cf. A308969 (prime divisors without repetition), A308970 (column 1 = first / smallest term of each row), A308971 (last / greatest term in each row).

%K nonn,tabf

%O 1,2

%A _M. F. Hasler_, Jul 03 2019