A308971 Largest prime factor of A001008(n), numerator of n-th harmonic number; a(1) = 1.

1, 3, 11, 5, 137, 7, 11, 761, 7129, 61, 863, 509, 919, 1117, 41233, 8431, 1138979, 39541, 7440427, 11167027, 18858053, 227, 583859, 467183, 312408463, 34395742267, 215087, 375035183, 4990290163, 17783, 2667653736673, 535919, 199539368321, 15088528003, 137121586897

Offset

1,2

Comments

Initial terms coincide with A120299 = greatest prime factor of Stirling numbers of first kind A000254. They differ when the unreduced denominator of H(n), equal to n!, is divisible by this factor, i.e., A120299(n) <= n. Can this ever happen?

Links

Amiram Eldar, Table of n, a(n) for n = 1..325

Formula

a(n) = A006530(A001008(n)). - Amiram Eldar, Feb 24 2020

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., therefore this sequence = 1, 3, 11, 5, 137, 7, 11, 761, 7129, 61, ...

Mathematica

Array[FactorInteger[Numerator@HarmonicNumber[#]][[-1, 1]] &, 35] (* Michael De Vlieger, Jul 04 2019 *)

Prog

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

Crossrefs

Cf. A001008, A006530.

Cf. A308967 (number of prime factors), A308968 (table of factorization), A308969 (table of prime divisors), A308970 (smallest prime factor) of A001008(n).

Sequence in context: A242223 A308969 A308970 * A120299 A341217 A094900

Adjacent sequences: A308968 A308969 A308970 * A308972 A308973 A308974

Keyword

nonn

Author

M. F. Hasler, Jul 03 2019

Status

approved