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 A162538 The smallest number with an arithmetic mean of divisors equal to n; 0 if nonexistent. 3

%I

%S 1,3,5,7,0,11,13,21,17,19,0,23,45,39,29,31,0,46,37,57,41,43,0,47,0,99,

%T 53,91,0,59,61,93,86,67,116,71,73,111,125,79,0,83,0,129,89,0,0,141,97,

%U 0,101,103,0,107,109,188,113,0,0,158,169,183,166,127,261,131,0,201,137

%N The smallest number with an arithmetic mean of divisors equal to n; 0 if nonexistent.

%C a(n) is the smallest k such that sigma(k)/tau(k) = A000203(k)/A000005(k) = n.

%C Zeros occur if n is in A157847 (i.e., not in A157846).

%e a(7)= 13 because sigma(13)=14 and tau(13)= 2 so 14/2 = 7.

%e a(8)= 21 because sigma(21)=32 and tau(21)= 4 so 32/4 = 8.

%t Table[SelectFirst[Range[10^3],n*DivisorSigma[0,#]==DivisorSigma[1,#]&],{n,70}]/.(Missing["NotFound"]->0) (* _Harvey P. Dale_, Dec 14 2015 *)

%Y Cf. A003601.

%K nonn

%O 1,2

%A _Claudio Meller_, Jul 05 2009

%E Edited by _R. J. Mathar_, Aug 07 2009

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Last modified June 7 01:26 EDT 2020. Contains 334836 sequences. (Running on oeis4.)