A336426 - OEIS

%I #7 Jul 27 2020 00:24:33

%S 3,5,6,7,9,10,11,13,14,15,17,18,19,20,21,22,23,25,26,27,28,29,30,31,

%T 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,55,56,

%U 57,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76

%N Numbers that cannot be written as a product of superprimorials {2, 12, 360, 75600, ...}.

%C The n-th superprimorial is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1).

%e We have 288 = 2*12*12 so 288 is not in the sequence.

%t chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];

%t facsusing[s_,n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#,d]&)/@Select[facsusing[Select[s,Divisible[n/d,#]&],n/d],Min@@#>=d&],{d,Select[s,Divisible[n,#]&]}]];

%t Select[Range[100],facsusing[Array[chern,30],#]=={}&]

%Y A181818 is the complement.

%Y A336497 is the version for superfactorials.

%Y A001055 counts factorizations.

%Y A006939 lists superprimorials or Chernoff numbers.

%Y A022915 counts permutations of prime indices of superprimorials.

%Y A317829 counts factorizations of superprimorials.

%Y A336417 counts perfect-power divisors of superprimorials.

%Y Cf. A000325, A005117, A076954, A124010, A294068, A336419, A336420, A336421, A336496, A336500, A336568.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jul 26 2020