A318978 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A318978

Heinz numbers of integer partitions with a common divisor > 1.

3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 37, 39, 41, 43, 47, 49, 53, 57, 59, 61, 63, 65, 67, 71, 73, 79, 81, 83, 87, 89, 91, 97, 101, 103, 107, 109, 111, 113, 115, 117, 121, 125, 127, 129, 131, 133, 137, 139, 147, 149, 151, 157, 159, 163, 167, 169

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

OFFSET

1,1

COMMENTS

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

Is this the same as A305078 without the leading 2? - R. J. Mathar, Sep 08 2018

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

The sequence of all integer partitions with a common divisor begins: (2), (3), (4), (2,2), (5), (6), (7), (8), (4,2), (9), (3,3), (2,2,2), (10), (11), (12), (6,2), (13), (14), (15), (4,4), (16), (8,2), (17), (18), (4,2,2), (6,3), (19), (20), (21), (22), (2,2,2,2), (23), (10,2), (24), (6,4), (25).

MATHEMATICA

Select[Range[100], GCD@@PrimePi/@If[#==1, {}, FactorInteger[#]][[All, 1]]>1&]

CROSSREFS

Cf. A000837, A018783, A056239, A289508, A289509, A296150, A298748.

Sequence in context: A265166 A366251 A336620 * A327755 A322903 A363691

Adjacent sequences: A318975 A318976 A318977 * A318979 A318980 A318981

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 06 2018

STATUS

approved