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A300486 Number of relatively prime or monic partitions of n. 17
1, 2, 3, 4, 7, 8, 15, 18, 28, 35, 56, 64, 101, 120, 168, 210, 297, 348, 490, 583, 776, 946, 1255, 1482, 1952, 2335, 2981, 3581, 4565, 5387, 6842, 8119, 10086, 12013, 14863, 17527, 21637, 25525, 31083, 36695, 44583, 52256, 63261, 74171, 88932, 104303, 124754 (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).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

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

FORMULA

a(n > 1) = 1 + A000837(n) = 1 + Sum_{d|n} mu(d) * A000041(n/d).

EXAMPLE

The a(6) = 8 relatively prime or monic partitions are (6), (51), (411), (321), (3111), (2211), (21111), (111111). Missing from this list are (42), (33), (222).

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Or[Length[#]===1, GCD@@#===1]&]], {n, 20}]

PROG

(PARI) a(n)={(n > 1) + sumdiv(n, d, moebius(d)*numbpart(n/d))} \\ Andrew Howroyd, Aug 29 2018

CROSSREFS

Cf. A000837, A001383, A063834, A093637, A196545, A281113, A289501, A300383, A301462, A301467, A301480, A302094, A302698, A302915, A302916, A302917.

Sequence in context: A015927 A097110 A116961 * A120611 A092063 A227007

Adjacent sequences:  A300483 A300484 A300485 * A300487 A300488 A300489

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 15 2018

STATUS

approved

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Last modified December 10 14:27 EST 2019. Contains 329896 sequences. (Running on oeis4.)