login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323519 a(n) is the number of ways to fill a square matrix with the multiset of prime factors of n, if the number of prime factors (counted with multiplicity) is a perfect square, and a(n) = 0 otherwise. 5
1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 4, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 6, 1, 0, 0, 4, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 4, 0, 4, 0, 0, 1, 12, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 12, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,24

LINKS

Table of n, a(n) for n=1..86.

FORMULA

If A001222(n) is a perfect square, then a(n) = A008480(n). Otherwise, a(n) = 0.

EXAMPLE

The a(60) = 12 matrices:

  [2 2] [2 2] [2 3] [2 3] [2 5] [2 5] [3 2] [3 2] [3 5] [5 2] [5 2] [5 3]

  [3 5] [5 3] [2 5] [5 2] [2 3] [3 2] [2 5] [5 2] [2 2] [2 3] [3 2] [2 2]

MATHEMATICA

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

Table[If[IntegerQ[Sqrt[PrimeOmega[n]]], Length[Permutations[primeMS[n]]], 0], {n, 100}]

CROSSREFS

Positions of 0's are A323521.

Positions of 1's are A323520.

Cf. A000290, A008480, A026478, A056239, A089299, A103198, A112798, A120732, A323433, A323525, A323531.

Sequence in context: A061859 A289110 A287287 * A276580 A108708 A290322

Adjacent sequences:  A323516 A323517 A323518 * A323520 A323521 A323522

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 17 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 November 13 02:59 EST 2019. Contains 329085 sequences. (Running on oeis4.)