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A336496 Products of superfactorials (A000178). 7
1, 2, 4, 8, 12, 16, 24, 32, 48, 64, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 1728, 2048, 2304, 3072, 3456, 4096, 4608, 6144, 6912, 8192, 9216, 12288, 13824, 16384, 18432, 20736, 24576, 27648, 32768, 34560, 36864, 41472, 49152, 55296 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First differs from A317804 in having 34560, which is the first term with more than two distinct prime factors.

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

The sequence of terms together with their prime indices begins:

    1: {}

    2: {1}

    4: {1,1}

    8: {1,1,1}

   12: {1,1,2}

   16: {1,1,1,1}

   24: {1,1,1,2}

   32: {1,1,1,1,1}

   48: {1,1,1,1,2}

   64: {1,1,1,1,1,1}

   96: {1,1,1,1,1,2}

  128: {1,1,1,1,1,1,1}

  144: {1,1,1,1,2,2}

  192: {1,1,1,1,1,1,2}

  256: {1,1,1,1,1,1,1,1}

  288: {1,1,1,1,1,2,2}

  384: {1,1,1,1,1,1,1,2}

  512: {1,1,1,1,1,1,1,1,1}

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[1000], facsusing[Rest[Array[supfac, 30]], #]!={}&]

CROSSREFS

A001013 is the version for factorials, with complement A093373.

A181818 is the version for superprimorials, with complement A336426.

A336497 is the complement.

A000178 lists superfactorials.

A001055 counts factorizations.

A006939 lists superprimorials or Chernoff numbers.

A049711 is the minimum prime multiplicity in A000178.

A174605 is the maximum prime multiplicity in A000178.

A303279 counts prime factors of superfactorials.

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: A069519 A087980 A181818 * A317804 A328524 A322447

Adjacent sequences:  A336493 A336494 A336495 * A336497 A336498 A336499

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 03 2020

STATUS

approved

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Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)