A336735 Products of elements of A304711.

1, 2, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 33, 34, 35, 36, 38, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 58, 60, 62, 64, 66, 68, 69, 70, 72, 74, 75, 76, 77, 80, 82, 84, 85, 86, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 106

Offset: 1

Author

Gus Wiseman, Aug 02 2020

Keywords

• nonn

Comments

A304711 lists numbers whose distinct prime indices are pairwise coprime.

First differs from A304711 in having 84.

Examples

			The sequence of terms together with their prime indices begins:
      1: {}            28: {1,1,4}         52: {1,1,6}
      2: {1}           30: {1,2,3}         54: {1,2,2,2}
      4: {1,1}         32: {1,1,1,1,1}     55: {3,5}
      6: {1,2}         33: {2,5}           56: {1,1,1,4}
      8: {1,1,1}       34: {1,7}           58: {1,10}
     10: {1,3}         35: {3,4}           60: {1,1,2,3}
     12: {1,1,2}       36: {1,1,2,2}       62: {1,11}
     14: {1,4}         38: {1,8}           64: {1,1,1,1,1,1}
     15: {2,3}         40: {1,1,1,3}       66: {1,2,5}
     16: {1,1,1,1}     44: {1,1,5}         68: {1,1,7}
     18: {1,2,2}       45: {2,2,3}         69: {2,9}
     20: {1,1,3}       46: {1,9}           70: {1,3,4}
     22: {1,5}         48: {1,1,1,1,2}     72: {1,1,1,2,2}
     24: {1,1,1,2}     50: {1,3,3}         74: {1,12}
     26: {1,6}         51: {2,7}           75: {2,3,3}
		

Links

• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

A181818 is the version for superprimorials, with complement A336426.

A336496 is the version for superfactorials, with complement A336497.

A336620 is the complement.

A000837 counts relatively prime partitions, with strict case A007360.

A001055 counts factorizations.

A302696 lists numbers with coprime prime indices.

A304711 lists numbers with coprime distinct prime indices.

Cf. A001221, A007360, A007916, A056239, A112798, A302569, A327516, A333228, A335238, A335239, A335240, A336424, A336497, A336736.

Programs

Mathematica

nn=100;
dat=Select[Range[nn],CoprimeQ@@PrimePi/@First/@FactorInteger[#]&];
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,#]&]}]];
Select[Range[nn],facsusing[dat,#]!={}&]