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A325505
Heinz number of the set of Heinz numbers of all strict integer partitions of n.
7
2, 3, 5, 143, 493, 62651, 26718511, 22017033127, 44220524211551, 52289759420183033963, 546407750301194131199484983, 8362548333129019658779663581495109, 1828111016191440393570169991636207115709029581, 1059934964500839879758659437301868941873808925011368355891
OFFSET
0,1
COMMENTS
The Heinz number of a set or sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
Also Heinz numbers of rows of A246867 (squarefree numbers arranged by sum of prime indices A056239).
FORMULA
a(n) = Product_{i = 1..A000009(n)} prime(A246867(n,i)).
A001221(a(n)) = A001222(a(n)) = A000009(n).
A056239(a(n)) = A147655(n).
A003963(a(n)) = A325506(n).
EXAMPLE
The strict integer partitions of 5 are {(5), (4,1), (3,2)}, with Heinz numbers {11,14,15}, with Heinz number prime(11)*prime(14)*prime(15) = 62651, so a(6) = 62651.
The sequence of terms together with their prime indices begins:
2: {1}
3: {2}
5: {3}
143: {5,6}
493: {7,10}
62651: {11,14,15}
26718511: {13,21,22,30}
22017033127: {17,26,33,35,42}
44220524211551: {19,34,39,55,66,70}
52289759420183033963: {23,38,51,65,77,78,105,110}
546407750301194131199484983: {29,46,57,85,91,102,130,154,165,210}
MATHEMATICA
Table[Times@@Prime/@(Times@@Prime/@#&/@Select[IntegerPartitions[n], UnsameQ@@#&]), {n, 7}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 07 2019
STATUS
approved