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A276188 Numbers n>1 such that the number of odd divisors of n-1 is odd and is equal to the number of odd divisors of n+1. 1
3, 99, 577, 3363 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A334723 A167582 A068420 * A180350 A293952 A303826
KEYWORD
nonn,more
AUTHOR
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)