A164522 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).

1, 27089, 115289, 233729, 2529090, 2880989, 14059709, 17192909, 17540250, 18693990, 34902630, 54722249, 58517910, 82200689, 83087730, 92991990, 93623250, 93862230, 96578369, 111681990, 112244369, 155120129, 206450369, 269626769, 293182469, 303206310, 324764910

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

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

27089 is in the sequence since A000593(27089) = A000593(27089 + 1) = 27456.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000593, A002961, A064115, A064125, A293183, A306985.

Sequence in context: A159995 A253339 A236825 * A037045 A186481 A210073

Adjacent sequences: A164519 A164520 A164521 * A164523 A164524 A164525

Keyword

nonn

Author

Amiram Eldar, Aug 12 2019

Status

approved