A361937 - OEIS

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.

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

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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

Amiram Eldar, Table of n, a(n) for n = 1..52

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

Cf. A000005, A246600, A355670, A359080, A359082, A359083.

Similar sequences: A307870, A335832, A361807.

Sequence in context: A087079 A252757 A230579 * A009694 A275816 A097000

Adjacent sequences: A361934 A361935 A361936 * A361938 A361939 A361940

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Mar 31 2023

STATUS

approved