A341676 - OEIS

A341676

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

2, 3, 2, 5, 3, 7, 3, 5, 11, 13, 7, 5, 17, 19, 5, 7, 11, 23, 5, 13, 7, 29, 31, 11, 17, 7, 37, 19, 13, 41, 7, 43, 11, 23, 47, 7, 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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

We define a divisor d|n to be superior if d >= n/d. Superior divisors are counted by A038548 and listed by A161908. Numbers with a superior prime divisor are listed by A063538.

LINKS

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

EXAMPLE

The sequence of superior prime divisors begins: {}, {2}, {3}, {2}, {5}, {3}, {7}, {}, {3}, {5}, {11}, {}, {13}, {7}, {5}, {}, {17}, {}, {19}, {5}, ...

MATHEMATICA

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

PROG

(PARI) lista(nmax) = {my(p); for(n = 1, nmax, p = select(x -> (x^2 >= n), factor(n)[, 1]); if(#p == 1, print1(p[1], ", "))); } \\ Amiram Eldar, Nov 01 2024

CROSSREFS

Inferior versions are A107286 (smallest), A217581 (largest), A056608.

These divisors (superior prime) are counted by A341591.

The strictly superior version is A341643.

A001221 counts prime divisors, with sum A001414.

A033676 selects the greatest inferior divisor.

A033677 selects the smallest superior divisor.

A038548 counts superior (or inferior) divisors.

A056924 counts strictly superior (or strictly inferior) divisors.

A060775 selects the greatest strictly inferior divisor.

A063538/A063539 have/lack a superior prime divisor.

A070038 adds up superior divisors.