A164557 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).

3, 6, 7, 10, 22, 31, 46, 58, 69, 82, 106, 127, 140, 154, 160, 166, 178, 226, 262, 286, 346, 358, 382, 466, 478, 502, 562, 586, 718, 748, 781, 838, 862, 886, 982, 1001, 1018, 1066, 1186, 1282, 1299, 1306, 1318, 1366, 1438, 1486, 1522, 1614, 1618, 1672, 1704, 1822

Offset: 1

Author

Amiram Eldar, Aug 12 2019

Keywords

• nonn

Examples

			3 is in the sequence since A002131(3) = A002131(3 + 1) = 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Daeyeoul Kim and Abdelmejid Bayad, Convolution identities for twisted Eisenstein series and twisted divisor functions, Fixed Point Theory and Applications 2013, No. 1 (2013), Article 81, alternative link.
• Daeyeoul Kim, Nazli Yildiz Ikikardes, Yan Li, and Lianrong Ma, On the Problem sigma_od(n) = sigma_od(n+ 1), Filomat, Vol. 33, No. 2 (2019), pp. 543-559.

Crossrefs

Cf. A002131, A002961, A064115, A064125, A293183, A306985.

Programs

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

Mathematica

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