|
|
A341593
|
|
Number of superior prime-power divisors of n.
|
|
24
|
|
|
0, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 4, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
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
|
|
|
EXAMPLE
|
The superior prime-power divisors (columns) of selected n:
n = 4374 5103 6144 7500 9000
----------------------------
81 81 128 125 125
243 243 256 625
729 729 512
2187 1024
2048
|
|
MATHEMATICA
|
Table[Length[Select[Divisors[n], PrimePowerQ[#]&&#>=n/#&]], {n, 100}]
|
|
CROSSREFS
|
Positions of zeros after the first are A051283.
The version for prime instead of prime-power divisors is A341591.
The version for squarefree instead of prime-power divisors is A341592.
Dominates A341644 (the strictly superior case).
The version for odd instead of prime-power divisors is A341675.
The strictly inferior version is A341677.
A001222 counts prime-power divisors.
A033677 selects the smallest superior divisor.
A038548 counts superior (or inferior) divisors.
A056924 counts strictly superior (or strictly inferior) divisors.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|