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

1,1

Comments

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

Links

Table of n, a(n) for n=1..66.

Example

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

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], #]=={}&]

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.

Sequence in context: A254614 A320698 A182834 * A336497 A116883 A256543

Adjacent sequences: A336423 A336424 A336425 * A336427 A336428 A336429

Keyword

nonn

Author

Gus Wiseman, Jul 26 2020

Status

approved