|
Search: id:A102187
|
|
|
| A102187 |
|
Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer). |
|
+0
1
|
|
| 1, 2, 3, 3, 4, 6, 7, 6, 6, 9, 10, 7, 8, 9, 12, 10, 15, 9, 16, 12, 12, 19, 15, 14, 21, 12, 22, 14, 13, 18, 24, 19, 18, 27, 15, 18, 15, 20, 30, 14, 31, 24, 21, 18, 34, 21, 24, 18, 36, 37, 24, 21, 40, 42, 27, 33, 30, 45, 28, 28, 32, 36, 30, 21, 49, 26, 51, 27, 52, 24, 54, 55, 27, 38
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Values of sigma(n)/tau(n) on the terms of A003601, where tau(n) (A000005) is the number of divisors of n and sigma(n) (A000203) is the sum of the divisors of n.
|
|
REFERENCES
|
O. Ore, On the averages of the divisors of a number, Amer. Math. Monthly, 55 (1948), 615-619.
|
|
FORMULA
|
a(n)=sigma(A003601(n))/tau(A003601(n)).
|
|
EXAMPLE
|
The first four terms are 1,2,3,amd 3, being the averages of the divisors of the first four arithmetic numbers, 1,3,5, and 6, respectively. Indeed, 1/1=1, (1+3)/2=2, (1+5)/2=3, and (1+2+3+6)/4=3.
|
|
MAPLE
|
with(numtheory): p:=proc(n) if type(sigma(n)/tau(n), integer)=true then sigma(n)/tau(n) else fi end: seq(p(n), n=1..130);
|
|
CROSSREFS
|
Cf. A003601, A000005, A000203.
Sequence in context: A100989 A023158 A120882 this_sequence A133610 A029033 A041003
Adjacent sequences: A102184 A102185 A102186 this_sequence A102188 A102189 A102190
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 16 2005
|
|
|
Search completed in 0.002 seconds
|
