

A325131


Heinz numbers of integer partitions where the set of distinct parts is disjoint from the set of distinct multiplicities.


24



1, 3, 4, 5, 7, 8, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 64, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 100, 101, 103, 105, 107, 109, 111, 113, 115, 119, 121, 123, 127
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OFFSET

1,2


COMMENTS

The enumeration of these partitions by sum is given by A114639.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers where the prime indices are disjoint from the prime exponents.


LINKS



EXAMPLE

The sequence of terms together with their prime indices begins:
1: {}
3: {2}
4: {1,1}
5: {3}
7: {4}
8: {1,1,1}
11: {5}
13: {6}
15: {2,3}
16: {1,1,1,1}
17: {7}
19: {8}
21: {2,4}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
31: {11}
32: {1,1,1,1,1}
33: {2,5}


MATHEMATICA

Select[Range[100], Intersection[PrimePi/@First/@FactorInteger[#], Last/@FactorInteger[#]]=={}&]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



