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

1,2

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.

Links

Table of n, a(n) for n=1..55.

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[#]&]

Crossrefs

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

Sequence in context: A141603 A262748 A138786 * A139392 A274720 A338318

Adjacent sequences: A305730 A305731 A305732 * A305734 A305735 A305736

Keyword

nonn

Author

Gus Wiseman, Jun 22 2018

Status

approved