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A102187
Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer).
10
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
OFFSET
1,2
COMMENTS
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.
LINKS
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,and 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);
MATHEMATICA
a003601[n_Integer] :=
Select[Range[n], IntegerQ[DivisorSigma[1, #]/DivisorSigma[0, #]] &]; a102187[n_Integer] :=
Map[DivisorSigma[1, #]/DivisorSigma[0, #] &, a003601[n]]; a102187[200] (* Michael De Vlieger, Aug 05 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 16 2005
STATUS
approved