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A363693
Terms of A363691 with a record number of divisors.
1
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
1,1
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, ... .
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]
PROG
(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, ", "))); }
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jun 16 2023
STATUS
approved