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A341646 Numbers with a strictly superior squarefree divisor. 25
2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Table of n, a(n) for n=1..66.

EXAMPLE

60 has three strictly superior squarefree divisors {10,15,30} so 60 is in the sequence.

MATHEMATICA

Select[Range[100], Function[n, Select[Divisors[n], SquareFreeQ[#]&&#>n/#&]!={}]]

CROSSREFS

The version for prime instead of squarefree divisors is A064052.

The version for prime-power instead of squarefree divisors is the complement of A051283.

The weakly superior version is the complement of A059172.

The version for odd instead of squarefree divisors is A116883.

These are the positions of non-zero terms in A341595.

The complement is A341645.

A001221 counts prime divisors, with sum A001414.

A005117 lists squarefree numbers.

A038548 counts superior (or inferior) divisors.

A056924 counts strictly superior (or strictly inferior) divisors.

A140271 selects the smallest strictly superior divisor.

A207375 list central divisors.

A341673 lists strictly superior divisors.

- Inferior: A033676, A063962, A066839, A069288, A161906, A217581, A333749.

- Superior: A033677, A063538, A063539, A070038, A072500, A116882, A161908, A341591, A341592, A341593, A341675, A341676.

- Strictly Inferior: A060775, A070039, A333805, A333806, A341596, A341674.

- Strictly Superior: A048098, A238535, A341594, A341595, A341643, A341644.

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

Sequence in context: A175082 A007916 A052485 * A109421 A335433 A212167

Adjacent sequences:  A341643 A341644 A341645 * A341647 A341648 A341649

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 22 2021

STATUS

approved

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Last modified June 13 22:55 EDT 2021. Contains 345016 sequences. (Running on oeis4.)