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A361937
Numbers k with record values of the ratio A000005(k)/A246600(k) between the total number of divisors of k and the number of divisors d of k such that the bitwise OR of k and d is equal to k.
3
1, 2, 4, 8, 16, 32, 64, 128, 256, 336, 420, 840, 1680, 3360, 6720, 7560, 15120, 30240, 60480, 95760, 120960, 176400, 191520, 257040, 352800, 383040, 514080, 1028160, 1681680, 2056320, 2998800, 3112200, 5525520, 5997600, 6224400, 8353800, 12448800, 16216200, 24897600
OFFSET
1,2
COMMENTS
This sequence is infinite since the ratio A000005(k)/A246600(k) is unbounded. For example, if k = 2^m then A000005(k)/A246600(k) = m+1.
All the terms except for 1 are in A355670.
LINKS
EXAMPLE
The ratios A000005(k)/A246600(k) for k = 1, 2, 3 and 4 are 1, 2, 1 and 3. The record values, 1, 2 and 3, occur at 1, 2 and 4, the first 3 terms of this sequence.
MATHEMATICA
r[n_] := DivisorSigma[0, n]/DivisorSum[n, Boole[BitOr[#, n] == n] &];
seq[kmax_] := Module[{rm = 0, k = 1, s = {}, r1}, Do[r1 = r[k]; If[r1 > rm, rm = r1; AppendTo[s, k]], {k, 1 , kmax}]; s]; seq[10^6]
PROG
(PARI) r(n) = numdiv(n)/sumdiv(n, d, bitor(d, n) == n);
lista(kmax) = {my(rm = 0, r1); for(k = 1, kmax, r1 = r(k); if(r1 > rm, rm = r1; print1(k, ", "))); }
CROSSREFS
Similar sequences: A307870, A335832, A361807.
Sequence in context: A087079 A252757 A230579 * A009694 A275816 A097000
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Mar 31 2023
STATUS
approved