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A045780 Least value with A045779(n) factorizations into distinct factors.

%I A045780 #23 Oct 25 2024 09:35:54
%S A045780 1,6,12,64,24,256,48,512,60,96,2048,144,210,120,216,180,384,288,16384,
%T A045780 240,432,420,65536,1536,360,480,900,864,3072,1152,1296,2310,524288,
%U A045780 6144,960,720,840,2304,1728,1080,1260,2592,2097152,1800,4608,24576,4194304,1440,3456
%N A045780 Least value with A045779(n) factorizations into distinct factors.
%H A045780 David A. Corneth, <a href="/A045780/b045780.txt">Table of n, a(n) for n = 1..953</a>
%e A045780 From _Gus Wiseman_, Jan 11 2020: (Start)
%e A045780 The strict factorizations of a(n) for n = 1..9:
%e A045780   ()  (6)    (12)   (64)     (24)     (256)     (48)     (512)     (60)
%e A045780       (2*3)  (2*6)  (2*32)   (3*8)    (4*64)    (6*8)    (8*64)    (2*30)
%e A045780              (3*4)  (4*16)   (4*6)    (8*32)    (2*24)   (16*32)   (3*20)
%e A045780                     (2*4*8)  (2*12)   (2*128)   (3*16)   (2*256)   (4*15)
%e A045780                              (2*3*4)  (2*4*32)  (4*12)   (4*128)   (5*12)
%e A045780                                       (2*8*16)  (2*3*8)  (2*4*64)  (6*10)
%e A045780                                                 (2*4*6)  (2*8*32)  (2*5*6)
%e A045780                                                          (4*8*16)  (3*4*5)
%e A045780                                                                    (2*3*10)
%e A045780 (End)
%e A045780 30 is not in the sequence even though A045779(30) = 5. As 24 is the smallest k such that A045779(k) = 5 we have a(m) = 24 where m is such that A045779(m) = 5 which turns out to be m = 5 (not every positive integer is in A045779). So a(5) = 24. - _David A. Corneth_, Oct 24 2024
%Y A045780 All terms belong to A025487.
%Y A045780 The non-strict version is A045783.
%Y A045780 The sorted version is A330997.
%Y A045780 Factorizations are A001055 with image A045782 and complement A330976.
%Y A045780 Strict factorizations are A045778 with image A045779 and complement A330975.
%Y A045780 The least number with exactly n strict factorizations is A330974(n).
%Y A045780 Cf. A033833, A318286, A330972, A330973, A330989.
%K A045780 nonn
%O A045780 1,2
%A A045780 _David W. Wilson_
%E A045780 More terms from _David A. Corneth_, Oct 24 2024