%I #28 Sep 08 2022 08:45:47
%S 3,6,7,10,22,31,46,58,69,82,106,127,140,154,160,166,178,226,262,286,
%T 346,358,382,466,478,502,562,586,718,748,781,838,862,886,982,1001,
%U 1018,1066,1186,1282,1299,1306,1318,1366,1438,1486,1522,1614,1618,1672,1704,1822
%N Numbers k such that s(k) = s(k+1), where s(k) is the sum of divisors d of k such that k/d is odd (A002131).
%H Amiram Eldar, <a href="/A164557/b164557.txt">Table of n, a(n) for n = 1..10000</a>
%H Daeyeoul Kim and Abdelmejid Bayad, <a href="https://doi.org/10.1186/1687-1812-2013-81">Convolution identities for twisted Eisenstein series and twisted divisor functions</a>, Fixed Point Theory and Applications 2013, No. 1 (2013), Article 81, <a href="https://core.ac.uk/download/pdf/81538924.pdf">alternative link</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 3 is in the sequence since A002131(3) = A002131(3 + 1) = 4.
%t f[p_, e_] := If[p == 2, p^e, (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, 2000}]; seq
%o (Magma) v:=[&+[d:d in Divisors(m)|IsOdd(Floor(m/d))] :m in [1..2000]]; [k:k in [1..#v-1]| v[k] eq v[k+1]]; // _Marius A. Burtea_, Aug 12 2019
%Y Cf. A002131, A002961, A064115, A064125, A293183, A306985.
%K nonn
%O 1,1
%A _Amiram Eldar_, Aug 12 2019