A302979 Powers of squarefree numbers whose prime indices are relatively prime. Heinz numbers of uniform partitions with relatively prime parts.

2, 4, 6, 8, 10, 14, 15, 16, 22, 26, 30, 32, 33, 34, 35, 36, 38, 42, 46, 51, 55, 58, 62, 64, 66, 69, 70, 74, 77, 78, 82, 85, 86, 93, 94, 95, 100, 102, 105, 106, 110, 114, 118, 119, 122, 123, 128, 130, 134, 138, 141, 142, 143, 145, 146, 154, 155, 158, 161, 165

Offset

1,1

Comments

A prime index of n is a number m such that prime(m) divides n. An integer partition is uniform if all parts appear with the same multiplicity. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

The number of uniform partitions of n with relatively prime parts is A078374(n).

Links

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

A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp.1-12.

Example

Sequence of all uniform relatively prime integer partitions begins (1), (11), (21), (111), (31), (41), (32), (1111), (51), (61), (321), (11111), (52), (71), (43), (2211).

Mathematica

Select[Range[200], And[GCD@@PrimePi/@FactorInteger[#][[All, 1]]===1, SameQ@@FactorInteger[#][[All, 2]]]&]

Crossrefs

Cf. A000009, A000837, A007916, A047966, A052409, A052410, A072774, A078374, A289023, A289509, A300486, A302491, A302796.

Sequence in context: A121832 A253241 A337972 * A006586 A260391 A022292

Adjacent sequences: A302976 A302977 A302978 * A302980 A302981 A302982

Keyword

nonn

Author

Gus Wiseman, Apr 16 2018

Status

approved