A341643 The unique strictly superior prime divisor of each number that has one.

2, 3, 5, 3, 7, 5, 11, 13, 7, 5, 17, 19, 5, 7, 11, 23, 13, 7, 29, 31, 11, 17, 7, 37, 19, 13, 41, 7, 43, 11, 23, 47, 17, 13, 53, 11, 19, 29, 59, 61, 31, 13, 11, 67, 17, 23, 71, 73, 37, 19, 11, 13, 79, 41, 83, 17, 43, 29, 11, 89, 13, 23, 31, 47, 19, 97, 11, 101

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..68.

Example

The strictly superior divisors of 15 are {5,15}, and A064052(10) = 15, so a(10) = 5.

Mathematica

Join@@Table[Select[Divisors[n], PrimeQ[#]&&#>n/#&], {n, 100}]

Crossrefs

The inferior version is (largest inferior prime divisor) is A217581.

These divisors (strictly superior prime) are counted by A341642.

a(n) is the unique prime divisor in row n of A341673, for each n in A064052.

The weak version is A341676.

A038548 counts superior (or inferior) divisors.

A048098 lists numbers without a strictly superior prime divisor.

A056924 counts strictly superior (or strictly inferior) divisors.

A063538/A063539 have/lack a superior prime divisors.

A140271 selects the smallest strictly superior divisor.

A207375 lists central divisors.

A238535 adds up strictly superior divisors.

A341591 counts superior prime divisors.

- Inferior: A033676, A063962, A066839, A069288, A161906, A333749, A333750.

- Superior: A033677, A051283, A059172, A070038, A116882, A116883, A161908, A341592, A341593, A341675.

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

- Strictly Superior: A341594, A341595, A341644, A341645, A341646.

Cf. A000005, A001055, A001221, A001248, A001414, A006530, A020639.

Sequence in context: A092386 A117369 A117366 * A073482 A318411 A225680

Adjacent sequences: A341640 A341641 A341642 * A341644 A341645 A341646

Keyword

nonn

Author

Gus Wiseman, Feb 20 2021

Status

approved