A343734 Highly composite 5-rough numbers: numbers that are divisible by neither 2 nor 3 whose number of divisors reaches a record.

1, 5, 25, 35, 175, 385, 1225, 1925, 5005, 13475, 25025, 85085, 175175, 425425, 1616615, 2977975, 8083075, 32757725, 37182145, 56581525, 185910725, 622396775, 929553625, 1301375075, 4647768125, 5391411025, 14315125825, 26957055125, 37739877175, 134785275625

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..208

Example

                                           number of
                                           divisors
   n   a(n)  prime factorization of a(n)    of a(n)
  --  -----  ----------------------------  ---------
   1      1  -                                  1
   2      5  5                                  2
   3     25  5^2                                3
   4     35  5   * 7                            4
   5    175  5^2 * 7                            6
   6    385  5   * 7   * 11                     8
   7   1225  5^2 * 7^2                          9
   8   1925  5^2 * 7   * 11                    12
   9   5005  5   * 7   * 11   * 13             16
  10  13475  5^2 * 7^2 * 11                    18
  11  25025  5^2 * 7   * 11   * 13             24
  12  85085  5   * 7   * 11   * 13   * 17      32

Crossrefs

Cf. A000005, A002182, A007310, A053624.

Sequence in context: A375154 A084967 A249827 * A279541 A361615 A070390

Adjacent sequences: A343731 A343732 A343733 * A343735 A343736 A343737

Keyword

nonn

Author

Jon E. Schoenfield, Jun 14 2021

Status

approved