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A336496
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Products of superfactorials (A000178).
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8
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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
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OFFSET
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1,2
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COMMENTS
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First differs from A317804 in having 34560, which is the first term with more than two distinct prime factors.
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LINKS
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EXAMPLE
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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}
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MATHEMATICA
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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]], #]!={}&]
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CROSSREFS
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A006939 lists superprimorials or Chernoff numbers.
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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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