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

1,2

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.

Links

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

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, 3, 761, ...

Prog

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

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).

Sequence in context: A352005 A242223 A308969 * A308971 A120299 A341217

Adjacent sequences: A308967 A308968 A308969 * A308971 A308972 A308973

Keyword

nonn

Author

M. F. Hasler, Jul 03 2019

Status

approved