%I #7 Sep 15 2018 15:46:31

%S 9,25,27,49,81,121,125,169,243,289,343,361,441,529,625,729,841,961,

%T 1331,1369,1521,1681,1849,2187,2197,2209,2401,2809,3125,3249,3481,

%U 3721,4225,4489,4913,5041,5329,6241,6561,6859,6889,7569,7921,8281,9261,9409,10201

%N Nonprime Heinz numbers of superperiodic integer partitions.

%C A subsequence of A001597.

%C A number n is in the sequence iff n = 2 or the prime indices of n have a common divisor > 1 and the Heinz number of the multiset of prime multiplicities of n, namely A181819(n), is already in the sequence.

%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

%e The sequence of partitions whose Heinz numbers belong to the sequence begins: (22), (33), (222), (44), (2222), (55), (333), (66), (22222), (77), (444), (88), (4422), (99), (3333), (222222).

%t supperQ[n_]:=Or[n==2,And[GCD@@PrimePi/@FactorInteger[n][[All,1]]>1,supperQ[Times@@Prime/@FactorInteger[n][[All,2]]]]];

%t Select[Range[10000],And[!PrimeQ[#],supperQ[#]]&]

%Y Cf. A001597, A056239, A072774, A181819, A182850, A289509, A296150, A298748, A304464, A305732, A317246, A317257, A319149, A319151.

%K nonn

%O 1,1

%A _Gus Wiseman_, Sep 12 2018