cp's OEIS Frontend

A336620 Numbers that are not a product of elements of A304711.

%I A336620 #13 Aug 06 2020 09:27:46
%S A336620 3,5,7,9,11,13,17,19,21,23,25,27,29,31,37,39,41,42,43,47,49,53,57,59,
%T A336620 61,63,65,67,71,73,78,79,81,83,87,89,91,97,101,103,105,107,109,111,
%U A336620 113,114,115,117,121,125,126,127,129,130,131,133,137,139,147,149
%N A336620 Numbers that are not a product of elements of A304711.
%C A336620 A304711 lists numbers whose distinct prime indices are pairwise coprime.
%C A336620 The first term divisible by 4 is a(421) = 1092.
%H A336620 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 A336620 The sequence of terms together with their prime indices begins:
%e A336620       3: {2}         39: {2,6}       78: {1,2,6}
%e A336620       5: {3}         41: {13}        79: {22}
%e A336620       7: {4}         42: {1,2,4}     81: {2,2,2,2}
%e A336620       9: {2,2}       43: {14}        83: {23}
%e A336620      11: {5}         47: {15}        87: {2,10}
%e A336620      13: {6}         49: {4,4}       89: {24}
%e A336620      17: {7}         53: {16}        91: {4,6}
%e A336620      19: {8}         57: {2,8}       97: {25}
%e A336620      21: {2,4}       59: {17}       101: {26}
%e A336620      23: {9}         61: {18}       103: {27}
%e A336620      25: {3,3}       63: {2,2,4}    105: {2,3,4}
%e A336620      27: {2,2,2}     65: {3,6}      107: {28}
%e A336620      29: {10}        67: {19}       109: {29}
%e A336620      31: {11}        71: {20}       111: {2,12}
%e A336620      37: {12}        73: {21}       113: {30}
%t A336620 nn=100;
%t A336620 dat=Select[Range[nn],CoprimeQ@@PrimePi/@First/@FactorInteger[#]&];
%t A336620 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 A336620 Select[Range[nn],facsusing[dat,#]=={}&]
%Y A336620 A336426 is the version for superprimorials, with complement A181818.
%Y A336620 A336497 is the version for superfactorials, with complement A336496.
%Y A336620 A336735 is the complement.
%Y A336620 A000837 counts relatively prime partitions, with strict case A007360.
%Y A336620 A001055 counts factorizations.
%Y A336620 A302696 lists numbers with coprime prime indices.
%Y A336620 A304711 lists numbers with coprime distinct prime indices.
%Y A336620 Cf. A007916, A112798, A302569, A327516, A333228, A335238, A335239, A335240, A335241, A336424, A336568, A336736.
%K A336620 nonn
%O A336620 1,1
%A A336620 _Gus Wiseman_, Aug 02 2020