

A158299


Numerators of averages of squares of the divisors of n.


3



1, 5, 5, 7, 13, 25, 25, 85, 91, 65, 61, 35, 85, 125, 65, 341, 145, 455, 181, 91, 125, 305, 265, 425, 217, 425, 205, 175, 421, 325, 481, 455, 305, 725, 325, 637, 685, 905, 425, 1105, 841, 625, 925, 427, 1183, 1325, 1105, 341, 817, 1085, 725, 595, 1405, 1025
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OFFSET

1,2


COMMENTS

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. [From Harvey P. Dale, Oct 13 2011]
If m and n are coprime, f(m*n) divides f(m)*f(n).  Robert Israel, Jul 15 2019


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)


MAPLE

f:= proc(n) local D;
D:= map(t > t^2, numtheory:divisors(n));
numer(convert(D, `+`)/nops(D));
end proc:
map(f, [$1..100]); # Robert Israel, Jul 15 2019


MATHEMATICA

Numerator[Mean/@(Divisors[Range[60]]^2)] (* Harvey P. Dale, Oct 13 2011 *)
Array[Numerator[DivisorSigma[2, #]/DivisorSigma[0, #]] &, 100]; (* Amiram Eldar, Jul 15 2019 *)


CROSSREFS

Cf. A001157, A000005, A158298 (for denominators).
Sequence in context: A078551 A247877 A252006 * A093307 A264388 A141392
Adjacent sequences: A158296 A158297 A158298 * A158300 A158301 A158302


KEYWORD

nonn,frac


AUTHOR

Jaroslav Krizek, Mar 15 2009


EXTENSIONS

Corrected and extended by Harvey P. Dale, Oct 13 2011


STATUS

approved



