The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A272691 Number of factorizations of the highly factorable numbers A033833. 3
 1, 2, 3, 4, 5, 7, 9, 12, 16, 19, 21, 29, 30, 31, 38, 47, 52, 57, 64, 77, 98, 105, 109, 118, 171, 212, 289, 382, 392, 467, 484, 662, 719, 737, 783, 843, 907, 1097, 1261, 1386, 1397, 1713, 1768, 2116, 2179, 2343, 3079, 3444, 3681, 3930, 5288, 5413, 5447 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS These are defined as record numbers of factorizations (A001055). - Gus Wiseman, Jan 13 2020 LINKS Amiram Eldar, Table of n, a(n) for n = 1..235 (terms 1..118 from E. R. Canfield et al.) R. E. Canfield, P. ErdÅ‘s and C. Pomerance, On a Problem of Oppenheim concerning "Factorisatio Numerorum", J. Number Theory 17 (1983), 1-28. Jun Kyo Kim, On highly factorable numbers, Journal Of Number Theory, Vol. 72, No. 1 (1998), pp. 76-91. FORMULA a(n) = A001055(A033833(n)). a(n) = A033834(n) + 1. - Amiram Eldar, Jun 07 2019 EXAMPLE From Gus Wiseman, Jan 13 2020: (Start) The a(1) = 1 through a(8) = 12 factorizations of highly factorable numbers:   ()  (4)    (8)      (12)     (16)       (24)       (36)       (48)       (2*2)  (2*4)    (2*6)    (2*8)      (3*8)      (4*9)      (6*8)              (2*2*2)  (3*4)    (4*4)      (4*6)      (6*6)      (2*24)                       (2*2*3)  (2*2*4)    (2*12)     (2*18)     (3*16)                                (2*2*2*2)  (2*2*6)    (3*12)     (4*12)                                           (2*3*4)    (2*2*9)    (2*3*8)                                           (2*2*2*3)  (2*3*6)    (2*4*6)                                                      (3*3*4)    (3*4*4)                                                      (2*2*3*3)  (2*2*12)                                                                 (2*2*2*6)                                                                 (2*2*3*4)                                                                 (2*2*2*2*3) (End) MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Length[facs[n]], {n, 100}]//.{foe___, x_, y_, afe___}/; x>=y:>{foe, x, afe} (* Gus Wiseman, Jan 13 2020 *) CROSSREFS The strict version is A331232. Factorizations are A001055, with image A045782 and complement A330976. Highly factorable numbers are A033833, with strict version A331200. Cf. A033834, A045778, A045783, A330972, A330973, A330998. Sequence in context: A039861 A039877 A291833 * A192433 A189083 A318156 Adjacent sequences:  A272688 A272689 A272690 * A272692 A272693 A272694 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 02 2016, following a suggestion from George Beck. STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 27 22:37 EDT 2020. Contains 338042 sequences. (Running on oeis4.)