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

Author

Emeric Deutsch, Feb 16 2005

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

Cf. A003601, A000005, A000203.

Programs

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 *)

Formula

a(n) = sigma(A003601(n))/tau(A003601(n)).