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A325500
Heinz number of the set of Heinz numbers of integer partitions of n. Heinz numbers of rows of A215366.
7
2, 3, 35, 2717, 22235779, 3163570326979, 51747966790650260753033, 188828800892079861898153036258130093, 2034903808706825942766196978067005215014684343665351270467, 75367279796373180679613801327275978589820813788234346991420766634058571423774287454563
OFFSET
0,1
COMMENTS
The Heinz number of a set of positive integers {y_1,...,y_k} is prime(y_1)*...*prime(y_k).
All terms are squarefree and pairwise relatively prime.
FORMULA
A001221(a(n)) = A001222(a(n)) = A000041(n).
A056239(a(n)) = A145519(n).
A003963(a(n)) = A325501(n).
A181819(A003963(a(n))) = A325507(n).
EXAMPLE
The integer partitions of 3 are {(3), (2,1), (1,1,1)}, with Heinz numbers {5,6,8}, with Heinz number prime(5)*prime(6)*prime(8) = 2717, so a(3) = 2717.
The sequence of terms together with their prime indices begins:
2: {1}
3: {2}
35: {3,4}
2717: {5,6,8}
22235779: {7,9,10,12,16}
3163570326979: {11,14,15,18,20,24,32}
51747966790650260753033: {13,21,22,25,27,28,30,36,40,48,64}
MATHEMATICA
Table[Times@@Prime/@(Times@@Prime/@#&/@IntegerPartitions[n]), {n, 0, 5}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 05 2019
STATUS
approved