login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A302094 Number of relatively prime or monic twice-partitions 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 (list; graph; refs; listen; history; text; internal format)
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: A173957 A048006 A211231 * A068818 A137173 A116544

Adjacent sequences:  A302091 A302092 A302093 * A302095 A302096 A302097

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 15 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)