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A302698 Number of integer partitions of n into relatively prime parts that are all greater than 1. 17
0, 0, 0, 0, 1, 0, 3, 2, 5, 4, 13, 7, 23, 18, 32, 33, 65, 50, 104, 92, 148, 153, 252, 226, 376, 376, 544, 570, 846, 821, 1237, 1276, 1736, 1869, 2552, 2643, 3659, 3887, 5067, 5509, 7244, 7672, 10086, 10909, 13756, 15168, 19195, 20735, 26237, 28708, 35418, 39207 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Two or more numbers are relatively prime if they have no common divisor other than 1. A single number is not considered relatively prime unless it is equal to 1 (which is impossible in this case).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

EXAMPLE

The first 10 terms count the following lists of integer partitions.

   1:

   2:

   3:

   4:

   5: (32)

   6:

   7: (52) (43) (322)

   8: (53) (332)

   9: (72) (54) (522) (432) (3222)

  10: (73) (532) (433) (3322)

MAPLE

b:= proc(n, i, g) option remember; `if`(n=0, `if`(g=1, 1, 0),

      `if`(i<2, 0, b(n, i-1, g)+b(n-i, min(n-i, i), igcd(g, i))))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=1..60);  # Alois P. Heinz, Apr 12 2018

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], FreeQ[#, 1]&&GCD@@#===1&]], {n, 30}]

CROSSREFS

Cf. A000837, A007359, A051424, A101268, A285572, A289508, A289509, A298748, A302568, A302569, A302696, A302697.

Sequence in context: A054080 A164379 A120332 * A205401 A329544 A095006

Adjacent sequences:  A302695 A302696 A302697 * A302699 A302700 A302701

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 11 2018

STATUS

approved

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)