A336497 Numbers that cannot be written as a product of superfactorials A000178.

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

First differs from A336426 in having 360.

Links

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

Example

The sequence of terms together with their prime indices begins:
     3: {2}        22: {1,5}        39: {2,6}
     5: {3}        23: {9}          40: {1,1,1,3}
     6: {1,2}      25: {3,3}        41: {13}
     7: {4}        26: {1,6}        42: {1,2,4}
     9: {2,2}      27: {2,2,2}      43: {14}
    10: {1,3}      28: {1,1,4}      44: {1,1,5}
    11: {5}        29: {10}         45: {2,2,3}
    13: {6}        30: {1,2,3}      46: {1,9}
    14: {1,4}      31: {11}         47: {15}
    15: {2,3}      33: {2,5}        49: {4,4}
    17: {7}        34: {1,7}        50: {1,3,3}
    18: {1,2,2}    35: {3,4}        51: {2,7}
    19: {8}        36: {1,1,2,2}    52: {1,1,6}
    20: {1,1,3}    37: {12}         53: {16}
    21: {2,4}      38: {1,8}        54: {1,2,2,2}

Mathematica

supfac[n_]:=Product[k!, {k, n}];
facsusing[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsusing[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]];
Select[Range[100], facsusing[Rest[Array[supfac, 30]], #]=={}&]

Crossrefs

A093373 is the version for factorials, with complement A001013.

A336426 is the version for superprimorials, with complement A181818.

A336496 is the complement.

A000178 lists superfactorials.

A001055 counts factorizations.

A006939 lists superprimorials or Chernoff numbers.

A049711 is the minimum prime multiplicity in A000178(n).

A174605 is the maximum prime multiplicity in A000178(n).

A303279 counts prime factors (with multiplicity) of superprimorials.

A317829 counts factorizations of superprimorials.

A322583 counts factorizations into factorials.

A325509 counts factorizations of factorials into factorials.

Cf. A000142, A000720, A007489, A011371, A022559, A022915, A027423, A034878, A034876, A076954, A115627, A294068.

Sequence in context: A320698 A182834 A336426 * A116883 A256543 A186145

Adjacent sequences: A336494 A336495 A336496 * A336498 A336499 A336500

Keyword

nonn

Author

Gus Wiseman, Aug 03 2020

Status

approved