A336496 - OEIS

%I #23 Aug 31 2020 04:24:00

%S 1,2,4,8,12,16,24,32,48,64,96,128,144,192,256,288,384,512,576,768,

%T 1024,1152,1536,1728,2048,2304,3072,3456,4096,4608,6144,6912,8192,

%U 9216,12288,13824,16384,18432,20736,24576,27648,32768,34560,36864,41472,49152,55296

%N Products of superfactorials (A000178).

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

%e The sequence of terms together with their prime indices begins:

%e     1: {}

%e     2: {1}

%e     4: {1,1}

%e     8: {1,1,1}

%e    12: {1,1,2}

%e    16: {1,1,1,1}

%e    24: {1,1,1,2}

%e    32: {1,1,1,1,1}

%e    48: {1,1,1,1,2}

%e    64: {1,1,1,1,1,1}

%e    96: {1,1,1,1,1,2}

%e   128: {1,1,1,1,1,1,1}

%e   144: {1,1,1,1,2,2}

%e   192: {1,1,1,1,1,1,2}

%e   256: {1,1,1,1,1,1,1,1}

%e   288: {1,1,1,1,1,2,2}

%e   384: {1,1,1,1,1,1,1,2}

%e   512: {1,1,1,1,1,1,1,1,1}

%t supfac[n_]:=Product[k!,{k,n}];

%t 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,#]&]}]];

%t Select[Range[1000],facsusing[Rest[Array[supfac,30]],#]!={}&]

%Y A001013 is the version for factorials, with complement A093373.

%Y A181818 is the version for superprimorials, with complement A336426.

%Y A336497 is the complement.

%Y A000178 lists superfactorials.

%Y A001055 counts factorizations.

%Y A006939 lists superprimorials or Chernoff numbers.

%Y A049711 is the minimum prime multiplicity in A000178.

%Y A174605 is the maximum prime multiplicity in A000178.

%Y A303279 counts prime factors of superfactorials.

%Y A317829 counts factorizations of superprimorials.

%Y A322583 counts factorizations into factorials.

%Y A325509 counts factorizations of factorials into factorials.

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Aug 03 2020