A341592 - OEIS

A341592

Number of squarefree superior divisors of n.

1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 0, 2, 1, 4, 1, 0, 2, 2, 2, 1, 1, 2, 2, 1, 1, 4, 1, 2, 1, 2, 1, 0, 1, 1, 2, 2, 1, 0, 2, 1, 2, 2, 1, 3, 1, 2, 1, 0, 2, 4, 1, 2, 2, 4, 1, 0, 1, 2, 1, 2, 2, 4, 1, 1, 0, 2, 1, 3, 2, 2, 2

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OFFSET

1,6

COMMENTS

We define a divisor d|n to be superior if d >= n/d. Superior divisors are counted by A038548 and listed by A161908.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

The strictly superior squarefree divisors (columns) of selected n:

1 6 8 30 60 210 420 630 1050 2310 4620 6930

------------------------------------------------------

1 3 . 6 10 15 21 30 35 55 70 105

6 10 15 21 30 35 42 66 77 110

15 30 30 35 42 70 70 105 154

30 35 42 70 105 77 110 165

42 70 105 210 105 154 210

70 105 210 110 165 231

105 210 154 210 330

210 165 231 385

210 330 462

231 385 770

330 462 1155

385 770 2310

462 1155

770 2310

1155

2310

MAPLE

with(numtheory):

a := n -> nops(select(d -> d*d >= n and issqrfree(d), divisors(n))):

seq(a(n), n = 1..88); # Peter Luschny, Feb 20 2021

MATHEMATICA

Table[Length[Select[Divisors[n], SquareFreeQ[#]&&#>=n/#&]], {n, 100}]

PROG

(PARI) a(n) = sumdiv(n, d, d^2 >= n && issquarefree(d)); \\ Amiram Eldar, Nov 01 2024

CROSSREFS

Positions of zeros are A059172.

The inferior version is A333749.

The version for prime instead of squarefree divisors is A341591.

The version for prime powers instead of squarefree divisors is A341593.

The strictly superior case is A341595.

The version for odd instead of squarefree divisors is A341675.

A001221 counts prime divisors, with sum A001414.

A033677 selects the smallest superior divisor.

A038548 counts superior (or inferior) divisors.

A056924 counts strictly superior (or strictly inferior) divisors.

A161908 lists superior divisors.

A207375 lists central divisors.

- Inferior: A033676, A063962, A066839, A069288, A161906, A217581, A333750.

- Superior: A051283, A063538, A063539, A070038, A116882, A116883, A341676.

- Strictly Inferior: A060775, A333805, A333806, A341596, A341674.

- Strictly Superior: A048098, A064052 A140271, A238535, A341594, A341642, A341643, A341644, A341645, A341646, A341673.

Cf. A000005, A000203, A001222, A001248, A006530, A020639, A112798.

Sequence in context: A237194 A143519 A344606 * A348952 A307778 A029376

Adjacent sequences: A341589 A341590 A341591 * A341593 A341594 A341595

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 19 2021

STATUS

approved