The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #8 May 07 2019 23:14:32
%S 1,2,6,28,340,3108,106932,2732340,236790060,19703562780,3419598096420,
%T 674127752953380,264134168649181380,95825592671995399620,
%U 67662122741507082338220,50556978553034312461203420,69259146896604886347745839660,104191622563656655781003976625020
%N Heinz number of the integer partition whose parts are the multiplicities in the multiset union of all integer partitions of n.
%C Also the Heinz number of row n of A066633.
%C The Heinz number of an integer partition or sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>
%F a(n) = Product_{i = 1..n} prime(A066633(n,i)).
%F a(n) = A181819(A003963(A325500(n))).
%F a(n) = A181819(A325501(n)).
%F A001222(a(n)) = n.
%F A056239(a(n)) = A006128(n).
%F For n > 0, A181819(a(n)) = A087009(n + 1).
%e The integer partitions of 4 are {(4), (3,1), (2,2), (2,1,1), (1,1,1,1)}, with multiset union {1,1,1,1,1,1,1,2,2,2,3,4}, with multiplicities (7,3,1,1), so a(4) = prime(7)*prime(3)*prime(1)*prime(1) = 340.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 6: {1,2}
%e 28: {1,1,4}
%e 340: {1,1,3,7}
%e 3108: {1,1,2,4,12}
%e 106932: {1,1,2,4,8,19}
%e 2732340: {1,1,2,3,6,11,30}
%e 236790060: {1,1,2,3,6,9,19,45}
%e 19703562780: {1,1,2,3,5,8,15,26,67}
%e 3419598096420: {1,1,2,3,5,8,13,21,41,97}
%e 674127752953380: {1,1,2,3,5,7,12,18,31,56,139}
%e 264134168649181380: {1,1,2,3,5,7,12,17,28,45,83,195}
%e 95825592671995399620: {1,1,2,3,5,7,11,16,25,38,63,112,272}
%e 67662122741507082338220: {1,1,2,3,5,7,11,16,24,35,55,87,160,373}
%t Table[Times@@Prime/@Length/@Split[Sort[Join@@IntegerPartitions[n]]],{n,0,15}]
%Y Cf. A001222, A003963, A006128, A007870, A056239, A066633, A087009, A112798, A215366, A302246, A325500, A325501, A325513.
%K nonn
%O 0,2
%A _Gus Wiseman_, May 07 2019