cp's OEIS Frontend

A336496 Products of superfactorials (A000178).

%I A336496 #23 Aug 31 2020 04:24:00
%S A336496 1,2,4,8,12,16,24,32,48,64,96,128,144,192,256,288,384,512,576,768,
%T A336496 1024,1152,1536,1728,2048,2304,3072,3456,4096,4608,6144,6912,8192,
%U A336496 9216,12288,13824,16384,18432,20736,24576,27648,32768,34560,36864,41472,49152,55296
%N A336496 Products of superfactorials (A000178).
%C A336496 First differs from A317804 in having 34560, which is the first term with more than two distinct prime factors.
%e A336496 The sequence of terms together with their prime indices begins:
%e A336496     1: {}
%e A336496     2: {1}
%e A336496     4: {1,1}
%e A336496     8: {1,1,1}
%e A336496    12: {1,1,2}
%e A336496    16: {1,1,1,1}
%e A336496    24: {1,1,1,2}
%e A336496    32: {1,1,1,1,1}
%e A336496    48: {1,1,1,1,2}
%e A336496    64: {1,1,1,1,1,1}
%e A336496    96: {1,1,1,1,1,2}
%e A336496   128: {1,1,1,1,1,1,1}
%e A336496   144: {1,1,1,1,2,2}
%e A336496   192: {1,1,1,1,1,1,2}
%e A336496   256: {1,1,1,1,1,1,1,1}
%e A336496   288: {1,1,1,1,1,2,2}
%e A336496   384: {1,1,1,1,1,1,1,2}
%e A336496   512: {1,1,1,1,1,1,1,1,1}
%t A336496 supfac[n_]:=Product[k!,{k,n}];
%t A336496 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 A336496 Select[Range[1000],facsusing[Rest[Array[supfac,30]],#]!={}&]
%Y A336496 A001013 is the version for factorials, with complement A093373.
%Y A336496 A181818 is the version for superprimorials, with complement A336426.
%Y A336496 A336497 is the complement.
%Y A336496 A000178 lists superfactorials.
%Y A336496 A001055 counts factorizations.
%Y A336496 A006939 lists superprimorials or Chernoff numbers.
%Y A336496 A049711 is the minimum prime multiplicity in A000178.
%Y A336496 A174605 is the maximum prime multiplicity in A000178.
%Y A336496 A303279 counts prime factors of superfactorials.
%Y A336496 A317829 counts factorizations of superprimorials.
%Y A336496 A322583 counts factorizations into factorials.
%Y A336496 A325509 counts factorizations of factorials into factorials.
%Y A336496 Cf. A000142, A000720, A007489, A011371, A022559, A022915, A027423, A034878, A034876, A076954, A115627, A294068.
%K A336496 nonn
%O A336496 1,2
%A A336496 _Gus Wiseman_, Aug 03 2020