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A304712 Number of integer partitions of n whose parts are all equal or whose distinct parts are pairwise coprime. 2
1, 1, 2, 3, 5, 7, 10, 14, 19, 25, 32, 43, 54, 70, 86, 105, 130, 162, 196, 240, 286, 339, 405, 485, 573, 674, 790, 922, 1072, 1252, 1456, 1685, 1939, 2226, 2557, 2923, 3349, 3822, 4347, 4931, 5593, 6335, 7170, 8092, 9105, 10233, 11495, 12903, 14458, 16169, 18063 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Two parts are coprime if they have no common divisor greater than 1.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

EXAMPLE

The a(6) = 10 partitions whose parts are all equal or whose distinct parts are pairwise coprime are (6), (51), (411), (33), (321), (3111), (222), (2211), (21111), (111111).

MAPLE

g:= proc(n, i, s) `if`(n=0, 1, `if`(i<1, 0,

      b(n, i, select(x-> x<=i, s))))

    end:

b:= proc(n, i, s) option remember; g(n, i-1, s)+(f->

     `if`(f intersect s={}, add(g(n-i*j, i-1, s union f)

        , j=1..n/i), 0))(numtheory[factorset](i))

    end:

a:= n-> g(n$2, {}):

seq(a(n), n=0..60);  # Alois P. Heinz, May 17 2018

MATHEMATICA

Table[Select[IntegerPartitions[n], Or[SameQ@@#, CoprimeQ@@Union[#]]&]//Length, {n, 20}]

CROSSREFS

Cf. A000837, A007359, A018783, A051424, A056239, A078374, A101268, A289508, A289509, A298748, A300486, A302569, A302696, A302698, A302796, A302797, A304709, A304711.

Sequence in context: A306473 A175846 A088585 * A175842 A008581 A172491

Adjacent sequences:  A304709 A304710 A304711 * A304713 A304714 A304715

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 17 2018

STATUS

approved

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Last modified January 22 13:41 EST 2020. Contains 331149 sequences. (Running on oeis4.)