A378267 Numbers k that have a record number of common divisors with sigma(k).

1, 6, 24, 120, 672, 4320, 26208, 30240, 524160, 2178540, 8714160, 8910720, 17428320, 45532800, 132723360, 208565280, 240589440, 470564640, 668304000, 1307124000, 5228496000, 10805558400, 14182439040, 31998395520, 159991977600

Offset

1,2

Comments

Indices of records in A073802.

This sequence is infinite since A073802 is unbounded. For example, for any odd number m we have A073802(2^(m-1)*(2^m-1)) >= A000005(m) and the number of divisors of odd numbers is unbounded.

The corresponding record values are 1, 4, 6, 16, 24, 40, 60, 96, 144, 216, 240, 336, ... .

a(26) <= 799959888000.

Links

Table of n, a(n) for n=1..25.

Mathematica

seq[kmax_] := Module[{d, dmax = 0, s = {}}, Do[d = DivisorSigma[0, GCD[k, DivisorSigma[1, k]]]; If[d > dmax, dmax = d; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[10^6]

Prog

(PARI) lista(kmax) = {my(d, dmax = 0); for(k = 1, kmax, d = numdiv(gcd(k, sigma(k))); if(d > dmax, dmax = d; print1(k, ", "))); }

Crossrefs

Cf. A000005, A000203 (sigma), A014567, A073802, A216793.

Sequence in context: A374722 A334328 A324064 * A050212 A369833 A354074

Adjacent sequences: A378264 A378265 A378266 * A378268 A378269 A378270

Keyword

nonn,more

Author

Amiram Eldar, Nov 21 2024

Status

approved