A298748 Heinz numbers of aperiodic (relatively prime multiplicities) integer partitions with relatively prime parts.

2, 6, 10, 12, 14, 15, 18, 20, 22, 24, 26, 28, 30, 33, 34, 35, 38, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 58, 60, 62, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 88, 90, 92, 93, 94, 95, 96, 98, 99, 102, 104, 105, 106, 108, 110, 112, 114

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..64.

Example

Sequence of partitions begins: (1), (21), (31), (211), (41), (32), (221), (311), (51), (2111), (61), (411), (321), (52), (71), (43), (81), (3111), (421), (511), (322), (91), (21111), (331), (72), (611), (2221), (53), (4111).

Mathematica

Select[Range[100], With[{t=Transpose[FactorInteger[#]]}, And[GCD@@PrimePi/@t[[1]]===1, GCD@@t[[2]]===1]]&] (* Gus Wiseman, Apr 14 2018 *)

Crossrefs

Cf. A000740, A000837, A007916, A052410, A064989, A100953, A289508, A289509, A296302, A300272.

Sequence in context: A133520 A346299 A099017 * A139799 A214586 A337687

Adjacent sequences: A298745 A298746 A298747 * A298749 A298750 A298751

Keyword

nonn

Author

Gus Wiseman, Mar 01 2018

Status

approved