A363693 Terms of A363691 with a record number of divisors.

3, 9, 21, 81, 105, 225, 945, 5265, 5985, 11025, 16065, 36225, 89505, 105105, 187425, 345345, 389025, 1044225, 2027025, 4189185, 6185025, 20307105, 27776385, 76039425, 107972865, 286711425, 402026625, 1853445825, 2440353825, 3807428625, 5106886785, 9449834625

Offset: 1

Author

Amiram Eldar, Jun 16 2023

Keywords

• nonn
• base

Comments

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.

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

Crossrefs

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

Programs

Mathematica

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]

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, ", "))); }