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

Author

Juri-Stepan Gerasimov, Aug 23 2016

Keywords

• nonn
• more

Comments

Conjecture: this sequence is finite.

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

Examples

			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.
		

Crossrefs

Cf. A275418, A275598, A276136.

Programs

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 ];

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 *)