cp's OEIS Frontend

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

%I A336497 #12 Aug 31 2020 04:23:38
%S A336497 3,5,6,7,9,10,11,13,14,15,17,18,19,20,21,22,23,25,26,27,28,29,30,31,
%T A336497 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,55,56,
%U A336497 57,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76
%N A336497 Numbers that cannot be written as a product of superfactorials A000178.
%C A336497 First differs from A336426 in having 360.
%e A336497 The sequence of terms together with their prime indices begins:
%e A336497      3: {2}        22: {1,5}        39: {2,6}
%e A336497      5: {3}        23: {9}          40: {1,1,1,3}
%e A336497      6: {1,2}      25: {3,3}        41: {13}
%e A336497      7: {4}        26: {1,6}        42: {1,2,4}
%e A336497      9: {2,2}      27: {2,2,2}      43: {14}
%e A336497     10: {1,3}      28: {1,1,4}      44: {1,1,5}
%e A336497     11: {5}        29: {10}         45: {2,2,3}
%e A336497     13: {6}        30: {1,2,3}      46: {1,9}
%e A336497     14: {1,4}      31: {11}         47: {15}
%e A336497     15: {2,3}      33: {2,5}        49: {4,4}
%e A336497     17: {7}        34: {1,7}        50: {1,3,3}
%e A336497     18: {1,2,2}    35: {3,4}        51: {2,7}
%e A336497     19: {8}        36: {1,1,2,2}    52: {1,1,6}
%e A336497     20: {1,1,3}    37: {12}         53: {16}
%e A336497     21: {2,4}      38: {1,8}        54: {1,2,2,2}
%t A336497 supfac[n_]:=Product[k!,{k,n}];
%t A336497 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 A336497 Select[Range[100],facsusing[Rest[Array[supfac,30]],#]=={}&]
%Y A336497 A093373 is the version for factorials, with complement A001013.
%Y A336497 A336426 is the version for superprimorials, with complement A181818.
%Y A336497 A336496 is the complement.
%Y A336497 A000178 lists superfactorials.
%Y A336497 A001055 counts factorizations.
%Y A336497 A006939 lists superprimorials or Chernoff numbers.
%Y A336497 A049711 is the minimum prime multiplicity in A000178(n).
%Y A336497 A174605 is the maximum prime multiplicity in A000178(n).
%Y A336497 A303279 counts prime factors (with multiplicity) of superprimorials.
%Y A336497 A317829 counts factorizations of superprimorials.
%Y A336497 A322583 counts factorizations into factorials.
%Y A336497 A325509 counts factorizations of factorials into factorials.
%Y A336497 Cf. A000142, A000720, A007489, A011371, A022559, A022915, A027423, A034878, A034876, A076954, A115627, A294068.
%K A336497 nonn
%O A336497 1,1
%A A336497 _Gus Wiseman_, Aug 03 2020