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A304711 Heinz numbers of integer partitions whose distinct parts are pairwise coprime. 19
2, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 33, 34, 35, 36, 38, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 58, 60, 62, 64, 66, 68, 69, 70, 72, 74, 75, 76, 77, 80, 82, 85, 86, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 106, 108, 110 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Two parts are coprime if they have no common divisor greater than 1. For partitions of length 1 note that (1) is coprime but (x) is not coprime for x > 1.

First differs from A289509 at a(24) = 44, A289509(24) = 42.

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

Sequence of all partitions whose distinct parts are pairwise coprime begins (1), (11), (21), (111), (31), (211), (41), (32), (1111), (221), (311), (51), (2111), (61), (411), (321), (11111), (52), (71), (43), (2211), (81), (3111).

MATHEMATICA

Select[Range[200], CoprimeQ@@PrimePi/@FactorInteger[#][[All, 1]]&]

CROSSREFS

Cf. A000837, A007359, A018783, A051424, A056239, A078374, A101268, A289508, A289509, A298748, A300486, A302569, A302696, A302698, A302796, A302797, A304709.

Sequence in context: A161207 A280877 A289509 * A324847 A302696 A195125

Adjacent sequences:  A304708 A304709 A304710 * A304712 A304713 A304714

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 17 2018

STATUS

approved

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Last modified February 24 01:16 EST 2020. Contains 332195 sequences. (Running on oeis4.)