A365264 a(n) is the smallest positive integer k whose number of divisors is larger than that of n.

2, 4, 4, 6, 4, 12, 4, 12, 6, 12, 4, 24, 4, 12, 12, 12, 4, 24, 4, 24, 12, 12, 4, 36, 6, 12, 12, 24, 4, 36, 4, 24, 12, 12, 12, 48, 4, 12, 12, 36, 4, 36, 4, 24, 24, 12, 4, 60, 6, 24, 12, 24, 4, 36, 12, 36, 12, 12, 4, 120, 4, 12, 24, 24, 12, 36, 4, 24, 12, 36, 4, 120, 4, 12, 24, 24, 12, 36, 4, 60

Offset: 1

Author

Hartmut F. W. Hoft, Aug 29 2023

Keywords

• nonn

Comments

The distinct values in this sequence together with 1 form A002182.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002182, A139770, A140635.

Programs

Mathematica

a365264[n_] := NestWhile[#+1&, 1, DivisorSigma[0, n]>=DivisorSigma[0, #]&]
a365264[{m_, n_}] := Map[a365264, Range[m, n]]
a365264[{1, 80}]

PARI

a(n) = my(k=1, nd=numdiv(n)); while(numdiv(k) <= nd, k++); k; \\ Michel Marcus, Aug 29 2023

Formula

a(n) = Min_{ k >= 1, sigma_0(k) > sigma_0(n) }, n>=1.

A002182(n+1) = a(a(...a(1))...) with n >= 0 iterations.