A302094 Number of relatively prime or monic twice-partitions of n.

1, 3, 6, 10, 27, 35, 113, 170, 396, 641, 1649, 2318, 5905, 9112, 18678, 32529, 69094, 106210, 227480, 363433, 705210, 1196190, 2325023, 3724233, 7192245, 11915884, 21857887, 36597843, 67406158, 109594872, 201747847, 333400746, 591125465, 987069077, 1743223350

Offset

1,2

Comments

A relatively prime or monic partition of n is an integer partition of n that is either of length 1 (monic) or whose parts have no common divisor other than 1 (relatively prime). Then a relatively prime or monic twice-partition of n is a choice of a relatively prime or monic partition of each part in a relatively prime or monic partition of n.

Links

Table of n, a(n) for n=1..35.

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

Example

The a(4) = 10 relatively prime or monic twice-partitions:
(4), (31), (211), (1111),
(3)(1), (21)(1), (111)(1),
(2)(1)(1), (11)(1)(1),
(1)(1)(1)(1).

Mathematica

ip[n_]:=ip[n]=Select[IntegerPartitions[n], Or[Length[#]===1, GCD@@#===1]&];
Table[Sum[Times@@Length/@ip/@ptn, {ptn, ip[n]}], {n, 10}]

Crossrefs

Cf. A000837, A001383, A063834, A093637, A196545, A281113, A289501, A300383, A300486, A301462, A301467, A301480, A302915, A302916, A302917.

Sequence in context: A048006 A364170 A211231 * A068818 A068866 A137173

Adjacent sequences: A302091 A302092 A302093 * A302095 A302096 A302097

Keyword

nonn

Author

Gus Wiseman, Apr 15 2018

Status

approved