login
A336620
Numbers that are not a product of elements of A304711.
1
3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 37, 39, 41, 42, 43, 47, 49, 53, 57, 59, 61, 63, 65, 67, 71, 73, 78, 79, 81, 83, 87, 89, 91, 97, 101, 103, 105, 107, 109, 111, 113, 114, 115, 117, 121, 125, 126, 127, 129, 130, 131, 133, 137, 139, 147, 149
OFFSET
1,1
COMMENTS
A304711 lists numbers whose distinct prime indices are pairwise coprime.
The first term divisible by 4 is a(421) = 1092.
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2} 39: {2,6} 78: {1,2,6}
5: {3} 41: {13} 79: {22}
7: {4} 42: {1,2,4} 81: {2,2,2,2}
9: {2,2} 43: {14} 83: {23}
11: {5} 47: {15} 87: {2,10}
13: {6} 49: {4,4} 89: {24}
17: {7} 53: {16} 91: {4,6}
19: {8} 57: {2,8} 97: {25}
21: {2,4} 59: {17} 101: {26}
23: {9} 61: {18} 103: {27}
25: {3,3} 63: {2,2,4} 105: {2,3,4}
27: {2,2,2} 65: {3,6} 107: {28}
29: {10} 67: {19} 109: {29}
31: {11} 71: {20} 111: {2,12}
37: {12} 73: {21} 113: {30}
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, #]=={}&]
CROSSREFS
A336426 is the version for superprimorials, with complement A181818.
A336497 is the version for superfactorials, with complement A336496.
A336735 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.
Sequence in context: A360114 A265166 A366251 * A318978 A327755 A322903
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 02 2020
STATUS
approved