OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
We define the multiset multiplicity kernel MMK(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 min(S) has multiplicity |S| in MMK(m). For example, MMK({1,1,2,2,3,4,5}) = {1,1,3,3,3}, and MMK({1,2,3,4,5,5,5,5}) = {1,1,1,1,5}. As an operation on multisets MMK is represented by A367579, and as an operation on their ranks it is represented by A367580.
FORMULA
Consists of 1 and all even terms of A072774 (powers of squarefree numbers).
EXAMPLE
We have MMK({1,1,2,2}) = {1,1} so 36 is in the sequence.
The terms together with their prime indices begin:
1: {}
2: {1}
4: {1,1}
6: {1,2}
8: {1,1,1}
10: {1,3}
14: {1,4}
16: {1,1,1,1}
22: {1,5}
26: {1,6}
30: {1,2,3}
32: {1,1,1,1,1}
34: {1,7}
36: {1,1,2,2}
38: {1,8}
42: {1,2,4}
MATHEMATICA
Select[Range[100], #==1||EvenQ[#]&&SameQ@@Last/@FactorInteger[#]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 30 2023
STATUS
approved