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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 17 11:26 EDT 2021. Contains 343064 sequences. (Running on oeis4.)