A276188 Numbers k > 1 such that the number of odd divisors of k-1 is odd and is equal to the number of odd divisors of k+1.

3, 99, 577, 3363

Offset

1,1

Comments

Conjecture: this sequence is finite.

Any further terms are greater than 10^10. - Charles R Greathouse IV, Aug 22 2016

Links

Table of n, a(n) for n=1..4.

Example

99 is in this sequence because there are 3 odd divisors 1, 7 and 49 of 98 and there are 3 odd divisors 1, 5 and 25 of 100, and 3 is odd.

Mathematica

odo[n_]:=Module[{c=Select[Divisors[n], OddQ]}, If[OddQ[Length[c]], Length[c], 0]]; Flatten[ Position[ Partition[Array[odo, 3500], 3, 1], _?(AllTrue[{#[[1]], #[[3]]}, OddQ]&&#[[1]]==#[[3]]&), 1, Heads->False]]+1 (* Harvey P. Dale, Apr 07 2023 *)

Prog

(Magma) [n: n in [2..100000] | NumberOfDivisors(2*(n-1))- NumberOfDivisors(n-1) eq NumberOfDivisors(2*(n+1))-NumberOfDivisors(n+1) and ((NumberOfDivisors(2*(n+1))- NumberOfDivisors(n+1)) mod 2) eq 1 ];

Crossrefs

Cf. A275418, A275598, A276136.

Sequence in context: A334723 A167582 A068420 * A180350 A293952 A303826

Adjacent sequences: A276185 A276186 A276187 * A276189 A276190 A276191

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Aug 23 2016

Status

approved