A308969 Table, read by rows: row n contains the prime divisors of A001008 (numerator of n-th harmonic number), without repetitions.

1, 3, 11, 5, 137, 7, 3, 11, 761, 7129, 11, 61, 97, 863, 13, 509, 29, 43, 919, 1049, 1117, 29, 41233, 17, 8431, 37, 1138979, 19, 39541, 37, 7440427, 5, 11167027, 18858053, 3, 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.

Links

Table of n, a(n) for n=1..45.

Example

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

Mathematica

Table[FactorInteger[Numerator[HarmonicNumber[n]]][[All, 1]], {n, 30}]// Flatten (* Harvey P. Dale, Sep 14 2020 *)

Prog

(PARI) row(n)={if(n>1, factor(A001008(n))[, 1]~, [1])}

Crossrefs

Cf. A001008.

Cf. A308967 (number of prime factors), A308968 (table of factorization), A308970 & A308971 (smallest & greatest prime factor) of A001008(n).

Sequence in context: A114234 A352005 A242223 * A308970 A308971 A120299

Adjacent sequences: A308966 A308967 A308968 * A308970 A308971 A308972

Keyword

nonn,tabf

Author

M. F. Hasler, Jul 03 2019

Status

approved