A308969 - OEIS

%I #16 Dec 09 2024 17:27:59

%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