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 A327599 Odd numbers k that have a divisor d such that sigma(d)*d is equal to k. 3

%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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Last modified March 22 22:37 EDT 2023. Contains 361434 sequences. (Running on oeis4.)