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A276188
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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.
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1
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OFFSET
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1,1
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COMMENTS
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Conjecture: this sequence is finite.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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 ];
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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