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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A285531 A111801 A108372 * A270342 A066542 A003310
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 01 2019
STATUS
approved

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Last modified June 20 03:21 EDT 2024. Contains 373512 sequences. (Running on oeis4.)