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%I #7 Jun 23 2018 14:21:03
%S 1,9,21,25,27,36,39,49,57,63,65,81,87,91,100,111,115,117,121,125,129,
%T 133,144,147,159,169,171,183,185,189,196,203,213,216,225,235,237,243,
%U 247,259,261,267,273,289,299,301,303,305,319,321,324,325,333,339,343
%N Heinz numbers of irreducible integer partitions. Nonprime numbers whose prime indices have a common divisor > 1 or such that 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). A prime index of n is a number m such that prime(m) divides n. A multiset m whose distinct elements are m_1, m_2, ..., m_k with multiplicities y_1, y_2, ..., y_k is reducible if either m is of size 1 or gcd(m_1, ..., m_k) = 1 and the multiset {y_1, ..., y_k} is also reducible.
%t rdzQ[n_]:=And[n>1,Or[PrimeQ[n],And[rdzQ[Times@@Prime/@FactorInteger[n][[All,2]]],GCD@@PrimePi/@FactorInteger[n][[All,1]]==1]]];
%t Select[Range[50],!rdzQ[#]&]
%Y Cf. A000837, A007916, A056239, A181819, A182850, A289508, A289509, A298748, A305563, A305731, A305732.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jun 22 2018
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