login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323584 Second Moebius transform of A000219. Number of plane partitions of n whose multiset of rows is aperiodic and whose multiset of columns is also aperiodic. 4
1, 1, 1, 4, 8, 22, 34, 84, 137, 271, 450, 857, 1373, 2483, 3993, 6823, 10990, 18332, 28966, 47328, 74286, 118614, 184755, 290781, 448010, 695986, 1063773, 1632100, 2474970, 3759610, 5654233, 8512307, 12710995, 18973247, 28139285, 41690830, 61423271, 90379782 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A multiset is aperiodic if its multiplicities are relatively prime.

Also the number of plane partitions of n whose multiset of rows is aperiodic and whose parts are relatively prime.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

The Moebius transform T of a sequence q is T(q)(n) = Sum_{d|n} mu(n/d) * q(d) where mu = A008683. The first Moebius transform of A000219 is A300275 and the third is A323585.

EXAMPLE

The a(4) = 8 plane partitions with aperiodic multisets of rows and columns:

  4   31   211

.

  3   21   111

  1   1    1

.

  2   11

  1   1

  1   1

The a(4) = 8 plane partitions with aperiodic multiset of rows and relatively prime parts:

  31   211   1111

.

  3   21   111

  1   1    1

.

  2   11

  1   1

  1   1

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];

ptnplane[n_]:=Union[Map[Reverse@*primeMS, Join@@Permutations/@facs[n], {2}]];

Table[Sum[Length[Select[ptnplane[Times@@Prime/@y], And[GCD@@Length/@Split[#]==1, And@@GreaterEqual@@@#, And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]], {y, Select[IntegerPartitions[n], GCD@@#==1&]}], {n, 10}]

CROSSREFS

Cf. A000219, A000837, A003293, A100953, A300275, A303546, A320802, A321390, A323585, A323587.

Sequence in context: A129794 A064503 A050482 * A200149 A153765 A003606

Adjacent sequences:  A323581 A323582 A323583 * A323585 A323586 A323587

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 19 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 17 14:57 EST 2020. Contains 330958 sequences. (Running on oeis4.)