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

1,1

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.

Example

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

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

Prog

(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

Crossrefs

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

Sequence in context: A262972 A115127 A258354 * A292608 A028754 A028795

Adjacent sequences: A164554 A164555 A164556 * A164558 A164559 A164560

Keyword

nonn

Author

Amiram Eldar, Aug 12 2019

Status

approved