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A327780 Number of integer partitions of n whose LCM is 2 * n. 4
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 12, 0, 0, 6, 0, 10, 32, 6, 0, 8, 0, 9, 0, 32, 0, 505, 0, 0, 108, 16, 147, 258, 0, 20, 170, 134, 0, 2030, 0, 140, 1865, 30, 0, 80, 0, 105, 350, 236, 0, 419, 500, 617, 474, 49, 0, 40966, 0, 56, 8225, 0, 785 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,15

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

The a(10) = 1 through a(20) = 10 partitions (A = 10) (empty columns not shown):

  (541)  (831)  (7421)   (A32)       (9432)     (A82)

                (74111)  (5532)      (9441)     (8552)

                         (6522)      (94221)    (A811)

                         (6531)      (94311)    (85421)

                         (A311)      (942111)   (85511)

                         (53322)     (9411111)  (852221)

                         (65211)                (854111)

                         (532221)               (8522111)

                         (533211)               (85211111)

                         (651111)               (851111111)

                         (5322111)

                         (53211111)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], LCM@@#==2*n&]], {n, 30}]

PROG

(PARI)

b(m, n)={my(d=divisors(m)); polcoef(1/prod(i=1, #d, 1 - x^d[i] + O(x*x^n)), n)}

a(n)={if(n<1, 0, sumdiv(2*n, d, moebius(d)*b(2*n/d, n)))} \\ Andrew Howroyd, Oct 09 2019

CROSSREFS

The Heinz numbers of these partitions are given by A327775.

Partitions whose LCM is a multiple of their sum are A327778.

Partitions whose LCM is equal to their sum are A074761.

Partitions whose LCM is greater than their sum are A327779.

Partitions whose LCM is less than their sum are A327781.

Cf. A018818, A290103, A316413, A326842.

Sequence in context: A110982 A079331 A265490 * A166489 A160367 A016736

Adjacent sequences:  A327777 A327778 A327779 * A327781 A327782 A327783

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 25 2019

STATUS

approved

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Last modified September 19 08:05 EDT 2021. Contains 347556 sequences. (Running on oeis4.)