A378267 - OEIS

%I #5 Nov 21 2024 05:40:27

%S 1,6,24,120,672,4320,26208,30240,524160,2178540,8714160,8910720,

%T 17428320,45532800,132723360,208565280,240589440,470564640,668304000,

%U 1307124000,5228496000,10805558400,14182439040,31998395520,159991977600

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

%C Indices of records in A073802.

%C 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.

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

%C a(26) <= 799959888000.

%t 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]

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

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

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Nov 21 2024