OFFSET
1,2
COMMENTS
First differs from A334298 in having 600 and lacking 180.
Also numbers whose minimum part in prime factorization is a unique mode.
If k is a term, then so are all powers of k. - Robert Israel, Sep 17 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
The prime factorization of 600 is 2*2*2*3*5*5, and 3 > max(1,2), so 600 is in the sequence.
The prime factorization of 180 is 2*2*3*3*5, but 2 <= max(2,1), so 180 is not in the sequence.
The terms together with their prime indices begin:
1: {} 29: {10} 67: {19}
2: {1} 31: {11} 68: {1,1,7}
3: {2} 32: {1,1,1,1,1} 71: {20}
4: {1,1} 37: {12} 72: {1,1,1,2,2}
5: {3} 40: {1,1,1,3} 73: {21}
7: {4} 41: {13} 76: {1,1,8}
8: {1,1,1} 43: {14} 79: {22}
9: {2,2} 44: {1,1,5} 80: {1,1,1,1,3}
11: {5} 45: {2,2,3} 81: {2,2,2,2}
12: {1,1,2} 47: {15} 83: {23}
13: {6} 48: {1,1,1,1,2} 84: {1,1,2,4}
16: {1,1,1,1} 49: {4,4} 88: {1,1,1,5}
17: {7} 52: {1,1,6} 89: {24}
19: {8} 53: {16} 92: {1,1,9}
20: {1,1,3} 56: {1,1,1,4} 96: {1,1,1,1,1,2}
23: {9} 59: {17} 97: {25}
24: {1,1,1,2} 60: {1,1,2,3} 99: {2,2,5}
25: {3,3} 61: {18} 101: {26}
27: {2,2,2} 63: {2,2,4} 103: {27}
28: {1,1,4} 64: {1,1,1,1,1,1} 104: {1,1,1,6}
MAPLE
filter:= proc(n) local F, i;
F:= ifactors(n)[2];
if nops(F) = 1 then return true fi;
i:= min[index](F[.., 1]);
andmap(t -> F[t, 2] < F[i, 2], {$1..nops(F)} minus {i})
end proc:
filter(1):= true:
select(filter, [$1..200]); # Robert Israel, Sep 17 2024
MATHEMATICA
Select[Range[100], First[Last/@FactorInteger[#]] > Max@@Rest[Last/@FactorInteger[#]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 14 2023
STATUS
approved