A308970 Smallest prime factor of A001008(n), numerator of n-th harmonic number; a(1) = 1.

1, 3, 11, 5, 137, 7, 3, 761, 7129, 11, 97, 13, 29, 1049, 29, 17, 37, 19, 37, 5, 18858053, 3, 761, 5, 109, 34395742267, 521, 29, 43, 31, 109, 2917, 269, 3583, 397, 37, 10839223, 199, 737281, 41, 85691034670497533, 7, 140473, 109, 1553, 47, 911, 7, 23982193, 61, 227, 53, 941, 5953

Offset: 1

Author

M. F. Hasler, Jul 03 2019

Keywords

• nonn

Comments

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

This is the first column of A308968 and A308969, which list the prime factors of A001008.

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..325

Crossrefs

Cf. A001008.

Cf. A308967 (number of prime factors), A308968 (table of factorization), A308969 (table of prime divisors), A308971 (greatest prime factor) of A001008(n).

Programs

Mathematica

FactorInteger[#][[1,1]]&/@Numerator[HarmonicNumber[Range[60]]] (* Harvey P. Dale, Jul 02 2025 *)

PARI

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