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

1,2

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.

Links

Table of n, a(n) for n=1..53.

M. F. Hasler, Rows 1 through 170.

Example

   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.

Prog

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

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).

Sequence in context: A210610 A188950 A357115 * A084466 A084462 A156320

Adjacent sequences: A308965 A308966 A308967 * A308969 A308970 A308971

Keyword

nonn,tabf

Author

M. F. Hasler, Jul 03 2019

Status

approved