cp's OEIS Frontend

A336735 Products of elements of A304711.

%I A336735 #7 Aug 06 2020 09:27:55
%S A336735 1,2,4,6,8,10,12,14,15,16,18,20,22,24,26,28,30,32,33,34,35,36,38,40,
%T A336735 44,45,46,48,50,51,52,54,55,56,58,60,62,64,66,68,69,70,72,74,75,76,77,
%U A336735 80,82,84,85,86,88,90,92,93,94,95,96,98,99,100,102,104,106
%N A336735 Products of elements of A304711.
%C A336735 A304711 lists numbers whose distinct prime indices are pairwise coprime.
%C A336735 First differs from A304711 in having 84.
%H A336735 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%e A336735 The sequence of terms together with their prime indices begins:
%e A336735       1: {}            28: {1,1,4}         52: {1,1,6}
%e A336735       2: {1}           30: {1,2,3}         54: {1,2,2,2}
%e A336735       4: {1,1}         32: {1,1,1,1,1}     55: {3,5}
%e A336735       6: {1,2}         33: {2,5}           56: {1,1,1,4}
%e A336735       8: {1,1,1}       34: {1,7}           58: {1,10}
%e A336735      10: {1,3}         35: {3,4}           60: {1,1,2,3}
%e A336735      12: {1,1,2}       36: {1,1,2,2}       62: {1,11}
%e A336735      14: {1,4}         38: {1,8}           64: {1,1,1,1,1,1}
%e A336735      15: {2,3}         40: {1,1,1,3}       66: {1,2,5}
%e A336735      16: {1,1,1,1}     44: {1,1,5}         68: {1,1,7}
%e A336735      18: {1,2,2}       45: {2,2,3}         69: {2,9}
%e A336735      20: {1,1,3}       46: {1,9}           70: {1,3,4}
%e A336735      22: {1,5}         48: {1,1,1,1,2}     72: {1,1,1,2,2}
%e A336735      24: {1,1,1,2}     50: {1,3,3}         74: {1,12}
%e A336735      26: {1,6}         51: {2,7}           75: {2,3,3}
%t A336735 nn=100;
%t A336735 dat=Select[Range[nn],CoprimeQ@@PrimePi/@First/@FactorInteger[#]&];
%t A336735 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 A336735 Select[Range[nn],facsusing[dat,#]!={}&]
%Y A336735 A181818 is the version for superprimorials, with complement A336426.
%Y A336735 A336496 is the version for superfactorials, with complement A336497.
%Y A336735 A336620 is the complement.
%Y A336735 A000837 counts relatively prime partitions, with strict case A007360.
%Y A336735 A001055 counts factorizations.
%Y A336735 A302696 lists numbers with coprime prime indices.
%Y A336735 A304711 lists numbers with coprime distinct prime indices.
%Y A336735 Cf. A001221, A007360, A007916, A056239, A112798, A302569, A327516, A333228, A335238, A335239, A335240, A336424, A336497, A336736.
%K A336735 nonn
%O A336735 1,2
%A A336735 _Gus Wiseman_, Aug 02 2020