OFFSET
1,2
COMMENTS
We define the multiset multiplicity cokernel MMC(m) of a multiset m by the following property, holding for all distinct multiplicities k >= 1. If S is the set of elements of multiplicity k in m, then max(S) has multiplicity |S| in MMC(m). For example, MMC({1,1,2,2,3,4,5}) = {2,2,5,5,5}, and MMC({1,2,3,4,5,5,5,5}) = {4,4,4,4,5}. As an operation on multisets MMC is represented by A367858, and as an operation on their ranks it is represented by A367859.
EXAMPLE
The terms together with their prime indices begin:
1: {} 23: {9} 47: {15}
2: {1} 26: {1,6} 52: {1,1,6}
3: {2} 28: {1,1,4} 53: {16}
5: {3} 29: {10} 58: {1,10}
6: {1,2} 30: {1,2,3} 59: {17}
7: {4} 31: {11} 60: {1,1,2,3}
10: {1,3} 34: {1,7} 61: {18}
11: {5} 37: {12} 62: {1,11}
12: {1,1,2} 38: {1,8} 63: {2,2,4}
13: {6} 41: {13} 66: {1,2,5}
14: {1,4} 42: {1,2,4} 67: {19}
17: {7} 43: {14} 68: {1,1,7}
19: {8} 44: {1,1,5} 71: {20}
20: {1,1,3} 45: {2,2,3} 73: {21}
22: {1,5} 46: {1,9} 74: {1,12}
MATHEMATICA
nn=100;
mmc[q_]:=With[{mts=Length/@Split[q]}, Sort[Table[Max@@Select[q, Count[q, #]==i&], {i, mts}]]];
qq=Table[Times@@mmc[Join@@ConstantArray@@@FactorInteger[n]], {n, nn}];
Select[Range[nn], FreeQ[Take[qq, #-1], qq[[#]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 03 2023
STATUS
approved