A341595 - OEIS

A341595

Number of strictly superior squarefree divisors of n.

0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 1, 1, 2, 2, 0, 1, 1, 1, 2, 2, 2, 1, 1, 0, 2, 0, 2, 1, 4, 1, 0, 2, 2, 2, 0, 1, 2, 2, 1, 1, 4, 1, 2, 1, 2, 1, 0, 0, 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 strictly superior if d > n/d. Strictly superior divisors are counted by A056924 and listed by A341673.

LINKS

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

EXAMPLE

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

n = 1 2 6 30 60 210 420 630 1050 2310 4620 6930

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

{} 2 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

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

The inferior version is A333749.

The non-strict version is A341592.

The version for odd instead of squarefree divisors is A341594.

The strictly inferior version is A341596.

The version for prime instead of squarefree divisors is A341642.

The version for prime-power instead of squarefree divisors is A341644.

Positions of 0's are A341645, with complement A341646.

A038548 counts superior (or inferior) divisors.

A056924 counts strictly superior (or strictly inferior) divisors.

A161908 lists superior divisors.

A207375 list central divisors.

A341673 lists strictly superior divisors.

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

- Superior: A033677, A051283, A059172, A063538, A063539, A070038, A116882, A116883, A341593, A341675, A341676.

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

- Strictly Superior: A048098, A064052 A140271, A238535, A341591, A341643.

Cf. A000005, A000203, A001221, A001222, A001248, A006530, A020639, A112798.

Sequence in context: A355817 A056169 A286852 * A369428 A125070 A125071

Adjacent sequences: A341592 A341593 A341594 * A341596 A341597 A341598

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 19 2021

STATUS

approved