A102187 Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer).

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

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), 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

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