cp's OEIS Frontend

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

%I A102187 #15 Aug 06 2014 01:37:49
%S A102187 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,
%T A102187 14,13,18,24,19,18,27,15,18,15,20,30,14,31,24,21,18,34,21,24,18,36,37,
%U A102187 24,21,40,42,27,33,30,45,28,28,32,36,30,21,49,26,51,27,52,24,54,55,27,38
%N A102187 Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer).
%C A102187 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.
%H A102187 Zak Seidov, <a href="/A102187/b102187.txt">Table of n, a(n) for n = 1..10000</a>
%H A102187 O. Ore, <a href="http://www.jstor.org/stable/2305616">On the averages of the divisors of a number</a>, Amer. Math. Monthly, 55 (1948), 615-619.
%F A102187 a(n) = sigma(A003601(n))/tau(A003601(n)).
%e A102187 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.
%p A102187 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);
%t A102187 a003601[n_Integer] :=
%t A102187 Select[Range[n], IntegerQ[DivisorSigma[1, #]/DivisorSigma[0, #]] &]; a102187[n_Integer] :=
%t A102187 Map[DivisorSigma[1, #]/DivisorSigma[0, #] &, a003601[n]]; a102187[200] (* _Michael De Vlieger_, Aug 05 2014 *)
%Y A102187 Cf. A003601, A000005, A000203.
%K A102187 nonn
%O A102187 1,2
%A A102187 _Emeric Deutsch_, Feb 16 2005