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A304713
Squarefree numbers whose prime indices are pairwise indivisible. Heinz numbers of strict integer partitions with pairwise indivisible parts.
33
1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35, 37, 41, 43, 47, 51, 53, 55, 59, 61, 67, 69, 71, 73, 77, 79, 83, 85, 89, 91, 93, 95, 97, 101, 103, 107, 109, 113, 119, 123, 127, 131, 137, 139, 141, 143, 145, 149, 151, 155, 157, 161, 163, 165, 167, 173
OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
EXAMPLE
Sequence of entries together with their corresponding multiset multisystems (see A302242) begins:
1: {}
2: {{}}
3: {{1}}
5: {{2}}
7: {{1,1}}
11: {{3}}
13: {{1,2}}
15: {{1},{2}}
17: {{4}}
19: {{1,1,1}}
23: {{2,2}}
29: {{1,3}}
31: {{5}}
33: {{1},{3}}
35: {{2},{1,1}}
MATHEMATICA
Select[Range[300], SquareFreeQ[#]&&Select[Tuples[PrimePi/@First/@FactorInteger[#], 2], UnsameQ@@#&&Divisible@@#&]==={}&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 17 2018
STATUS
approved