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A307895
Numbers whose prime exponents, starting from the largest prime factor through to the smallest, form an initial interval of positive integers.
7
1, 2, 3, 5, 7, 11, 12, 13, 17, 19, 20, 23, 28, 29, 31, 37, 41, 43, 44, 45, 47, 52, 53, 59, 61, 63, 67, 68, 71, 73, 76, 79, 83, 89, 92, 97, 99, 101, 103, 107, 109, 113, 116, 117, 124, 127, 131, 137, 139, 148, 149, 151, 153, 157, 163, 164, 167, 171, 172, 173
OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions whose multiplicities, starting from the largest part through to the smallest, form an initial interval of positive integers. The enumeration of these partitions by sum is given by A179269.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
3: {2}
5: {3}
7: {4}
11: {5}
12: {1,1,2}
13: {6}
17: {7}
19: {8}
20: {1,1,3}
23: {9}
28: {1,1,4}
29: {10}
31: {11}
37: {12}
41: {13}
43: {14}
44: {1,1,5}
45: {2,2,3}
MATHEMATICA
Select[Range[100], Last/@If[#==1, {}, FactorInteger[#]]==Range[PrimeNu[#], 1, -1]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 04 2019
STATUS
approved