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%I #10 Jul 07 2021 09:26:00
%S 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 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 3456,0,3600,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,24576
%N Least positive integer with exactly prime(n) factorizations into factors > 1, or 0 if no such integer exists.
%H 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 Factorizations of the initial positive terms are:
%e 4 8 16 24 60 96
%e 2*2 2*4 2*8 3*8 2*30 2*48
%e 2*2*2 4*4 4*6 3*20 3*32
%e 2*2*4 2*12 4*15 4*24
%e 2*2*2*2 2*2*6 5*12 6*16
%e 2*3*4 6*10 8*12
%e 2*2*2*3 2*5*6 2*6*8
%e 3*4*5 3*4*8
%e 2*2*15 4*4*6
%e 2*3*10 2*2*24
%e 2*2*3*5 2*3*16
%e 2*4*12
%e 2*2*3*8
%e 2*2*4*6
%e 2*3*4*4
%e 2*2*2*12
%e 2*2*2*2*6
%e 2*2*2*3*4
%e 2*2*2*2*2*3
%Y All positive terms belong to A025487 and also A033833.
%Y Factorizations are A001055, with image A045782, with complement A330976.
%Y Numbers whose number of partitions is prime are A046063.
%Y Numbers whose number of strict partitions is prime are A035359.
%Y Numbers whose number of set partitions is prime are A051130.
%Y Numbers with a prime number of factorizations are A330991.
%Y The least number with exactly 2^n factorizations is A330989(n).
%Y Cf. A001222, A045783, A325238, A330972, A330973, A330976, A330993, A330998.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jan 07 2020
%E More terms from _Jinyuan Wang_, Jul 07 2021