

A302094


Number of relatively prime or monic twicepartitions of n.


4



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
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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 twicepartition 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



EXAMPLE

The a(4) = 10 relatively prime or monic twicepartitions:
(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.


KEYWORD

nonn


AUTHOR



STATUS

approved



