A336426 Numbers that cannot be written as a product of superprimorials {2, 12, 360, 75600, ...}.

3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76

Offset: 1

Author

Gus Wiseman, Jul 26 2020

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

A181818 is the complement.

A336497 is the version for superfactorials.

A001055 counts factorizations.

A006939 lists superprimorials or Chernoff numbers.

A022915 counts permutations of prime indices of superprimorials.

A317829 counts factorizations of superprimorials.

A336417 counts perfect-power divisors of superprimorials.

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

Programs

Mathematica

chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
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,#]&]}]];
Select[Range[100],facsusing[Array[chern,30],#]=={}&]