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A339660 Number of strict integer partitions of n with no 1's and a part divisible by all the other parts. 3
1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 1, 3, 3, 3, 3, 5, 2, 5, 5, 4, 5, 7, 3, 5, 6, 5, 5, 9, 4, 7, 6, 6, 9, 11, 6, 9, 10, 9, 10, 12, 6, 11, 12, 10, 12, 16, 9, 15, 16, 12, 14, 18, 14, 16, 18, 14, 15, 22, 11, 16, 20, 13, 21, 23, 15, 21, 24, 21, 21, 31, 14, 24 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Alternative name: Number of strict integer partitions of n with no 1's that are empty or have greatest part divisible by all the other parts.

LINKS

Table of n, a(n) for n=0..74.

EXAMPLE

The a(n) partitions for n = 14, 12, 18, 24, 30, 39, 36:

  (14)     (12)    (18)      (24)        (30)        (39)          (36)

  (12,2)   (8,4)   (12,6)    (16,8)      (24,6)      (36,3)        (27,9)

  (8,4,2)  (9,3)   (15,3)    (18,6)      (25,5)      (26,13)       (30,6)

           (10,2)  (16,2)    (20,4)      (27,3)      (27,9,3)      (32,4)

                   (12,4,2)  (21,3)      (28,2)      (28,7,4)      (33,3)

                             (22,2)      (20,10)     (30,6,3)      (34,2)

                             (12,6,4,2)  (18,9,3)    (24,12,3)     (24,12)

                                         (24,4,2)    (24,8,4,3)    (24,8,4)

                                         (16,8,4,2)  (20,10,5,4)   (18,9,6,3)

                                                     (24,6,4,3,2)  (24,6,4,2)

                                                                   (20,10,4,2)

MATHEMATICA

Table[If[n==0, 1, Length[Select[IntegerPartitions[n], FreeQ[#, 1]&&UnsameQ@@#&&And@@IntegerQ/@(Max@@#/#)&]]], {n, 0, 30}]

CROSSREFS

The dual version is A098965 (non-strict: A083711).

The non-strict version is A339619 (Heinz numbers: complement of A343337).

The version with 1's allowed is A343347 (non-strict: A130689).

The case without a part dividing all the other parts is A343380.

A000009 counts strict partitions.

A000070 counts partitions with a selected part.

A015723 counts strict partitions with a selected part.

A018818 counts partitions into divisors (strict: A033630).

A167865 counts strict chains of divisors > 1 summing to n.

Cf. A083710, A097986, A098743, A200745, A264401, A339563, A341450, A343337, A343341, A343344, A343378.

Sequence in context: A030371 A029550 A091110 * A104659 A077197 A320510

Adjacent sequences:  A339657 A339658 A339659 * A339661 A339662 A339663

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 19 2021

STATUS

approved

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Last modified September 16 08:18 EDT 2021. Contains 347469 sequences. (Running on oeis4.)