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A325505 Heinz number of the set of Heinz numbers of all strict integer partitions of n. 7

%I

%S 2,3,5,143,493,62651,26718511,22017033127,44220524211551,

%T 52289759420183033963,546407750301194131199484983,

%U 8362548333129019658779663581495109,1828111016191440393570169991636207115709029581,1059934964500839879758659437301868941873808925011368355891

%N Heinz number of the set of Heinz numbers of all strict integer partitions of n.

%C The Heinz number of a set or sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%C Also Heinz numbers of rows of A246867 (squarefree numbers arranged by sum of prime indices A056239).

%H <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>

%F a(n) = Product_{i = 1..A000009(n)} prime(A246867(n,i)).

%F A001221(a(n)) = A001222(a(n)) = A000009(n).

%F A056239(a(n)) = A147655(n).

%F A003963(a(n)) = A325506(n).

%e 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.

%e The sequence of terms together with their prime indices begins:

%e 2: {1}

%e 3: {2}

%e 5: {3}

%e 143: {5,6}

%e 493: {7,10}

%e 62651: {11,14,15}

%e 26718511: {13,21,22,30}

%e 22017033127: {17,26,33,35,42}

%e 44220524211551: {19,34,39,55,66,70}

%e 52289759420183033963: {23,38,51,65,77,78,105,110}

%e 546407750301194131199484983: {29,46,57,85,91,102,130,154,165,210}

%t Table[Times@@Prime/@(Times@@Prime/@#&/@Select[IntegerPartitions[n],UnsameQ@@#&]),{n,7}]

%Y Cf. A001222, A003963, A015723, A056239, A066189, A112798, A145519, A147655, A215366, A246867, A325500 (non-strict version), A325504, A325506, A325512, A325513.

%K nonn

%O 0,1

%A _Gus Wiseman_, May 07 2019

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Last modified October 20 22:37 EDT 2019. Contains 328291 sequences. (Running on oeis4.)