A325501 - OEIS

%I #7 May 07 2019 17:37:52

%S 1,2,12,240,120960,638668800,15064408719360000,

%T 27259975545259032576000000,

%U 682714624600511148826789083611136000000000,2948964060660649503322235948384635104494106968064000000000000000

%N Product of Heinz numbers over all integer partitions of n.

%C Row-products of A215366 (positive integers arranged by sum of prime indices A056239).

%C The Heinz number of an integer partition (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 A001222(a(n)) = A006128(n).

%F A056239(a(n)) = A066186(n).

%F A003963(a(n)) = A007870(n).

%F A124010(a(n),i) = A066633(n,i).

%e The integer partitions of 3 are {(3), (2,1), (1,1,1)}, with Heinz numbers {5,6,8}, with product 240, so a(3) = 240.

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

%e           1: {}

%e           2: {1}

%e          12: {1,1,2}

%e         240: {1,1,1,1,2,3}

%e      120960: {1,1,1,1,1,1,1,2,2,2,3,4}

%e   638668800: {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,3,4,5}

%t Table[Times@@Prime/@(Join@@IntegerPartitions[n]),{n,0,5}]

%Y Cf. A003963, A006128, A007870, A008284, A056239, A066186, A066633, A112798, A118914, A124010, A145519, A215366, A325500, A325506, A325507.

%K nonn

%O 0,2

%A _Gus Wiseman_, May 06 2019