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%I
%S 1,117,775,2793,9801,16093,30927,88723,90675,137541,292537,326781,
%T 488125,732511,796797,954273,1882881,1926183,2164575,2896363,3500157,
%U 3618459,4985713,6725201,7595775,8042167,10380591,12326221,12472075,14076543,16092297,20456373,23968425,25774633
%N Odd numbers k that have a divisor d such that sigma(d)*d is equal to k.
%C We need d and sigma(d) odd which happens precisely when d is an odd square.
%H David A. Corneth, <a href="/A327599/b327599.txt">Table of n, a(n) for n = 1..10000</a>
%e As 9 * sigma(9) = 9 * (1 + 3 + 9) = 9 * 13 = 117 is odd, 117 is in the sequence.
%t Select[2Range[0, 9999] + 1, MemberQ[(DivisorSigma[1, #] * # &)/@Divisors[#], #] &] (* _Alonso del Arte_, Sep 18 2019 *)
%o (PARI) upto(n) = {my(res = List()); forstep(i = 1, sqrtnint(n, 4), 2, c = i^2*sigma(i^2); if(c <= n, listput(res, c))); listsort(res, 1); res}
%Y Odd terms of A327165.
%Y Cf. A064987.
%K nonn
%O 1,2
%A _David A. Corneth_, Sep 18 2019
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