cp's OEIS Frontend

A331201 Numbers k such that the number of factorizations of k into distinct factors > 1 is a prime number.

%I A331201 #4 Jan 13 2020 09:37:19
%S A331201 6,8,10,12,14,15,16,18,20,21,22,24,26,27,28,30,32,33,34,35,36,38,39,
%T A331201 40,42,44,45,46,48,50,51,52,54,55,56,57,58,62,63,65,66,68,69,70,74,75,
%U A331201 76,77,78,80,81,82,85,86,87,88,91,92,93,94,95,98,99,100,102
%N A331201 Numbers k such that the number of factorizations of k into distinct factors > 1 is a prime number.
%C A331201 First differs from A080257 in lacking 60.
%e A331201 Strict factorizations of selected terms:
%e A331201   (6)    (12)   (24)     (48)     (216)
%e A331201   (2*3)  (2*6)  (3*8)    (6*8)    (3*72)
%e A331201          (3*4)  (4*6)    (2*24)   (4*54)
%e A331201                 (2*12)   (3*16)   (6*36)
%e A331201                 (2*3*4)  (4*12)   (8*27)
%e A331201                          (2*3*8)  (9*24)
%e A331201                          (2*4*6)  (12*18)
%e A331201                                   (2*108)
%e A331201                                   (3*8*9)
%e A331201                                   (4*6*9)
%e A331201                                   (2*3*36)
%e A331201                                   (2*4*27)
%e A331201                                   (2*6*18)
%e A331201                                   (2*9*12)
%e A331201                                   (3*4*18)
%e A331201                                   (3*6*12)
%e A331201                                   (2*3*4*9)
%t A331201 strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A331201 Select[Range[100],PrimeQ[Length[strfacs[#]]]&]
%Y A331201 The version for strict integer partitions is A035359.
%Y A331201 The version for integer partitions is A046063.
%Y A331201 The version for set partitions is A051130.
%Y A331201 The non-strict version is A330991.
%Y A331201 Factorizations are A001055 with image A045782 and complement A330976.
%Y A331201 Strict factorizations are A045778 with image A045779 and complement A330975.
%Y A331201 Numbers whose number of strict factorizations is odd are A331230.
%Y A331201 Numbers whose number of strict factorizations is even are A331231.
%Y A331201 The least number with n strict factorizations is A330974(n).
%Y A331201 Cf. A001318, A045780, A318286, A328966, A330992, A330993, A330997, A331023/A331024, A331050, A331051, A331200, A331232.
%K A331201 nonn
%O A331201 1,1
%A A331201 _Gus Wiseman_, Jan 12 2020