cp's OEIS Frontend

A330992 Least positive integer with exactly prime(n) factorizations into factors > 1, or 0 if no such integer exists.

%I A330992 #10 Jul 07 2021 09:26:00
%S A330992 4,8,16,24,60,0,0,96,0,144,216,0,0,0,288,0,0,0,768,0,0,0,0,0,864,8192,
%T A330992 0,0,1080,0,0,0,1800,3072,0,0,0,0,0,0,0,2304,0,0,0,0,0,0,0,0,0,0,0,0,
%U A330992 3456,0,3600,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,24576
%N A330992 Least positive integer with exactly prime(n) factorizations into factors > 1, or 0 if no such integer exists.
%H A330992 R. E. Canfield, P. Erdős and C. Pomerance, <a href="http://math.dartmouth.edu/~carlp/PDF/paper39.pdf">On a Problem of Oppenheim concerning "Factorisatio Numerorum"</a>, J. Number Theory 17 (1983), 1-28.
%e A330992 Factorizations of the initial positive terms are:
%e A330992   4    8      16       24       60       96
%e A330992   2*2  2*4    2*8      3*8      2*30     2*48
%e A330992        2*2*2  4*4      4*6      3*20     3*32
%e A330992               2*2*4    2*12     4*15     4*24
%e A330992               2*2*2*2  2*2*6    5*12     6*16
%e A330992                        2*3*4    6*10     8*12
%e A330992                        2*2*2*3  2*5*6    2*6*8
%e A330992                                 3*4*5    3*4*8
%e A330992                                 2*2*15   4*4*6
%e A330992                                 2*3*10   2*2*24
%e A330992                                 2*2*3*5  2*3*16
%e A330992                                          2*4*12
%e A330992                                          2*2*3*8
%e A330992                                          2*2*4*6
%e A330992                                          2*3*4*4
%e A330992                                          2*2*2*12
%e A330992                                          2*2*2*2*6
%e A330992                                          2*2*2*3*4
%e A330992                                          2*2*2*2*2*3
%Y A330992 All positive terms belong to A025487 and also A033833.
%Y A330992 Factorizations are A001055, with image A045782, with complement A330976.
%Y A330992 Numbers whose number of partitions is prime are A046063.
%Y A330992 Numbers whose number of strict partitions is prime are A035359.
%Y A330992 Numbers whose number of set partitions is prime are A051130.
%Y A330992 Numbers with a prime number of factorizations are A330991.
%Y A330992 The least number with exactly 2^n factorizations is A330989(n).
%Y A330992 Cf. A001222, A045783, A325238, A330972, A330973, A330976, A330993, A330998.
%K A330992 nonn
%O A330992 1,1
%A A330992 _Gus Wiseman_, Jan 07 2020
%E A330992 More terms from _Jinyuan Wang_, Jul 07 2021