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

1, 3, 11, 5, 5, 137, 7, 7, 3, 11, 11, 761, 7129, 11, 11, 61, 97, 863, 13, 13, 509, 29, 43, 919, 1049, 1117, 29, 41233, 17, 17, 8431, 37, 1138979, 19, 19, 39541, 37, 7440427, 5, 11167027, 18858053, 3, 23, 23, 53, 227, 761, 583859, 5, 577, 467183, 109, 312408463

Offset: 1

Author

M. F. Hasler, Jul 03 2019

Keywords

• nonn
• tabf

Comments

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

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.

Examples

			   n | A001008(n) written as product of primes
-----+---------------------------------------------
   1 | 1 (empty product)
   2 | 3
   3 | 11
   4 | 5 * 5
   5 | 137
   6 | 7 * 7
   7 | 3 * 11 * 11
   8 | 761
   9 | 7129
  10 | 11 * 11 * 61
  11 | 97 * 863
  12 | 13 * 13 * 509
  13 | 29 * 43 * 919
  14 | 1049 * 1117
  15 | 29 * 41233
  16 | 17 * 17 * 8431
  17 | 37 * 1138979
  18 | 19 * 19 * 39541
  19 | 37 * 7440427
  20 | 5 * 11167027
etc.
		

Links

• M. F. Hasler, Rows 1 through 170.

Crossrefs

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

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

Programs

PARI

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