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

Author

Amiram Eldar, Nov 21 2024

Keywords

• nonn
• more

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.

Crossrefs

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

Programs

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]

PARI

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