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%I #6 Jan 08 2020 09:45:23
%S 1,4,12,0,72,0,480
%N Least positive integer with exactly 2^n factorizations into factors > 1, or 0 if no such integer exists.
%e The A001055(n) factorizations for n = 1, 4, 12, 72:
%e () (4) (12) (72)
%e (2*2) (2*6) (8*9)
%e (3*4) (2*36)
%e (2*2*3) (3*24)
%e (4*18)
%e (6*12)
%e (2*4*9)
%e (2*6*6)
%e (3*3*8)
%e (3*4*6)
%e (2*2*18)
%e (2*3*12)
%e (2*2*2*9)
%e (2*2*3*6)
%e (2*3*3*4)
%e (2*2*2*3*3)
%Y All nonzero terms belong to A025487 and also A033833.
%Y Factorizations are A001055, with image A045782.
%Y The least number with exactly n factorizations is A330973(n).
%Y Numbers whose number of factorizations is a power of 2 are A330977.
%Y The least number with exactly prime(n) factorizations is A330992(n).
%Y Cf. A002033, A045778, A045783, A318284, A330935, A330972, A330976, A330990, A330991, A331022.
%K nonn,more
%O 0,2
%A _Gus Wiseman_, Jan 07 2020