A392071 The records of min(d(k), d(k+2)), where d(k) is the number of divisors of k (A000005).

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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..36.

Formula

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

Example

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.

Mathematica

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 *)

Prog

(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)))

Crossrefs

Cf. A000005, A392006.

Sequence in context: A397956 A120370 A011866 * A321152 A292983 A174709

Adjacent sequences: A392068 A392069 A392070 * A392072 A392073 A392074

Keyword

nonn,more

Author

Zhicheng Wei, Feb 22 2026

Extensions

a(34)-a(36) from Michael S. Branicky, Mar 16 2026

Status

approved