

A102187


Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer).


9



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
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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

Zak Seidov, Table of n, a(n) for n = 1..10000
O. Ore, On the averages of the divisors of a number, Amer. Math. Monthly, 55 (1948), 615619.


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

Cf. A003601, A000005, A000203.
Sequence in context: A162627 A023158 A120882 * A133610 A256211 A265109
Adjacent sequences: A102184 A102185 A102186 * A102188 A102189 A102190


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Feb 16 2005


STATUS

approved



