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A328672 Number of integer partitions of n with relatively prime parts in which no two distinct parts are relatively prime. 5
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 4, 1, 4, 1, 1, 2, 7, 1, 6, 1, 3, 3, 10, 1, 9, 3, 5, 4, 17, 1, 23, 6, 7, 6, 20, 3, 36, 9, 15, 7, 45, 5, 56, 14, 17, 20, 65, 7, 83, 18, 40 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,32

COMMENTS

Positions of terms greater than 1 are {31, 37, 41, 43, 46, 47, 49, ...}.

A partition with no two distinct parts relatively prime is said to be intersecting.

LINKS

Table of n, a(n) for n=0..81.

FORMULA

a(n > 0) = A202425(n) + 1.

EXAMPLE

Examples:

  a(31) = 2:         a(46) = 2:

    (15,10,6)          (15,15,10,6)

    (1^31)             (1^46)

  a(37) = 3:         a(47) = 7:

    (15,12,10)         (20,15,12)

    (15,10,6,6)        (21,14,12)

    (1^37)             (20,15,6,6)

  a(41) = 4:           (21,14,6,6)

    (20,15,6)          (15,12,10,10)

    (21,14,6)          (15,10,10,6,6)

    (15,10,10,6)       (1^47)

    (1^41)           a(49) = 6:

  a(43) = 4:           (24,15,10)

    (18,15,10)         (18,15,10,6)

    (15,12,10,6)       (15,12,12,10)

    (15,10,6,6,6)      (15,12,10,6,6)

    (1^43)             (15,10,6,6,6,6)

                       (1^39)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], GCD@@#==1&&And[And@@(GCD[##]>1&)@@@Subsets[Union[#], {2}]]&]], {n, 0, 32}]

CROSSREFS

The Heinz numbers of these partitions are A328679.

The strict case is A318715.

The version for non-isomorphic multiset partitions is A319759.

Relatively prime partitions are A000837.

Intersecting partitions are A328673.

Cf. A078374, A285573, A289509, A291166, A303140, A305148, A316476, A326910, A326912.

Sequence in context: A220122 A101446 A259396 * A325355 A219093 A062760

Adjacent sequences:  A328669 A328670 A328671 * A328673 A328674 A328675

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 29 2019

STATUS

approved

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Last modified February 19 22:36 EST 2020. Contains 332061 sequences. (Running on oeis4.)