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%I #26 Sep 08 2022 08:45:47
%S 1,27089,115289,233729,2529090,2880989,14059709,17192909,17540250,
%T 18693990,34902630,54722249,58517910,82200689,83087730,92991990,
%U 93623250,93862230,96578369,111681990,112244369,155120129,206450369,269626769,293182469,303206310,324764910
%N Numbers k such that sigma_odd(k) = sigma_odd(k+1), where sigma_odd(k) is the sum of the odd divisors of k (A000593).
%H Amiram Eldar, <a href="/A164522/b164522.txt">Table of n, a(n) for n = 1..100</a>
%H Daeyeoul Kim, Nazli Yildiz Ikikardes, Yan Li, and Lianrong Ma, <a href="http://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/7068">On the Problem sigma_od(n) = sigma_od(n+ 1)</a>, Filomat, Vol. 33, No. 2 (2019), pp. 543-559.
%e 27089 is in the sequence since A000593(27089) = A000593(27089 + 1) = 27456.
%t f[p_, e_] := If[p == 2, 1, (p^(e+1)-1)/(p-1)]; s[1] = 1; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); s1=0; seq={}; Do[s2 = s[n]; If[s2 == s1, AppendTo[ seq, n-1]]; s1 = s2, {n, 1, 10^6}]; seq
%o (Magma) v:=[&+[d:d in Divisors(m)|IsOdd(d)] :m in [1..5000000]]; [k:k in [1..#v-1]| v[k] eq v[k+1]]; // _Marius A. Burtea_, Aug 12 2019
%Y Cf. A000593, A002961, A064115, A064125, A293183, A306985.
%K nonn
%O 1,2
%A _Amiram Eldar_, Aug 12 2019
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