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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 15 2018
STATUS
approved