A363693 - OEIS

%I #5 Jun 18 2023 02:02:30

%S 3,9,21,81,105,225,945,5265,5985,11025,16065,36225,89505,105105,

%T 187425,345345,389025,1044225,2027025,4189185,6185025,20307105,

%U 27776385,76039425,107972865,286711425,402026625,1853445825,2440353825,3807428625,5106886785,9449834625

%N Terms of A363691 with a record number of divisors.

%C Odd numbers k with a record number of divisors such that for all the nontrivial divisors d of k (i.e., divisors that are not 1 or k) the bitwise AND of k and d is not equal to d, or equivalently, the bitwise OR of k and d is not equal to k.

%C The corresponding record values are 2, 3, 4, 5, 8, 9, 16, 20, 24, 27, 32, 36, 40, 48, ... .

%t seq[kmax_] := Module[{s = {}, dm = 0, d1}, Do[d1 = DivisorSigma[0, k]; If[d1 > dm && DivisorSum[k, Boole[BitOr[#, k] == k] &] == 2, dm = d1; AppendTo[s, k]], {k, 1, kmax, 2}]; s]; seq[10^5]

%o (PARI) lista(kmax) = {my(dm = 0, d1); forstep(k = 1, kmax, 2, d1 = numdiv(k); if(d1 > dm && sumdiv(k, d, bitor(d, k) == k) == 2, dm = d1; print1(k, ", "))); }

%Y Cf. A000005, A359082, A359083, A361937, A363691, A363692.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Jun 16 2023