cp's OEIS Frontend

A158299 Numerators of averages of squares of the divisors of n.

%I A158299 #32 Sep 01 2025 18:27:41
%S A158299 1,5,5,7,13,25,25,85,91,65,61,35,85,125,65,341,145,455,181,91,125,305,
%T A158299 265,425,217,425,205,175,421,325,481,455,305,725,325,637,685,905,425,
%U A158299 1105,841,625,925,427,1183,1325,1105,341,817,1085,725,595,1405,1025
%N A158299 Numerators of averages of squares of the divisors of n.
%C A158299 Because Mathematica represents rational numbers with the smallest possible denominator, the terms of the sequence are numerators appropriate to such denominators. For example, the divisors of 3 are 1 and 3, so their squares are 1 and 9. The mean of those squares could be represented as 10/2 or 5/1. Mathematica selects the latter so a(3) is 5 rather than 10. - _Harvey P. Dale_, Oct 13 2011
%C A158299 If m and n are coprime, f(m*n) divides f(m)*f(n). - _Robert Israel_, Jul 15 2019
%H A158299 Amiram Eldar, <a href="/A158299/b158299.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%p A158299 f:= proc(n) local D;
%p A158299   D:= map(t -> t^2,numtheory:-divisors(n));
%p A158299   numer(convert(D,`+`)/nops(D));
%p A158299 end proc:
%p A158299 map(f, [$1..100]); # _Robert Israel_, Jul 15 2019
%t A158299 Numerator[Mean/@(Divisors[Range[60]]^2)] (* _Harvey P. Dale_, Oct 13 2011 *)
%t A158299 Array[Numerator[DivisorSigma[2, #]/DivisorSigma[0, #]] &, 100]; (* _Amiram Eldar_, Jul 15 2019 *)
%Y A158299 Cf. A001157, A000005, A158298 (for denominators).
%K A158299 nonn,frac,changed
%O A158299 1,2
%A A158299 _Jaroslav Krizek_, Mar 15 2009
%E A158299 Corrected and extended by _Harvey P. Dale_, Oct 13 2011