A392071 - OEIS

%I #53 Mar 16 2026 14:12:48

%S 1,2,3,4,5,6,8,10,12,14,16,18,20,24,28,32,40,42,48,60,64,72,80,96,108,

%T 120,128,150,160,168,192,240,256,288,320,336

%N The records of min(d(k), d(k+2)), where d(k) is the number of divisors of k (A000005).

%C The sequence min(d(n),d(n+2)) starts with 1, 2, 2, 3, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 5, 2, 6, 2, 4,... at n=1 and sets records of 1, 2, 3, 4, 5, 6, 8..., which creates this sequence.

%F a(n) = min(A000005(A392006(n)),A000005(A392006(n)+2)).

%e 18 is in this sequence because 18 is the value of min(d(880),d(882)), where d(880) = 20 and d(882) = 18. And there is no number k < 880 where min(d(k), d(k+2)) >= 18.

%t r = 0; {1}~Join~Reap[Do[If[# > r, r = #; Sow[#]] &[Min@ DivisorSigma[0, {n, n + 2}]], {n, 2, 2^20, 2}] ][[-1, 1]] (* _Michael De Vlieger_, Feb 24 2026 *)

%o (PARI) my(r=1); print1(r); for(n=2, 1e5, if(min(numdiv(n), numdiv(n+2))>r, r=min(numdiv(n), numdiv(n+2)); print1(", "r)))

%Y Cf. A000005, A392006.

%K nonn,more

%O 1,2

%A _Zhicheng Wei_, Feb 22 2026

%E a(34)-a(36) from _Michael S. Branicky_, Mar 16 2026