A305733 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.

1, 9, 21, 25, 27, 36, 39, 49, 57, 63, 65, 81, 87, 91, 100, 111, 115, 117, 121, 125, 129, 133, 144, 147, 159, 169, 171, 183, 185, 189, 196, 203, 213, 216, 225, 235, 237, 243, 247, 259, 261, 267, 273, 289, 299, 301, 303, 305, 319, 321, 324, 325, 333, 339, 343

Offset: 1

Author

Gus Wiseman, Jun 22 2018

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A000837, A007916, A056239, A181819, A182850, A289508, A289509, A298748, A305563, A305731, A305732.

Programs

Mathematica

rdzQ[n_]:=And[n>1,Or[PrimeQ[n],And[rdzQ[Times@@Prime/@FactorInteger[n][[All,2]]],GCD@@PrimePi/@FactorInteger[n][[All,1]]==1]]];
Select[Range[50],!rdzQ[#]&]