A135974 a(n) = the smallest integer m > n such that d(m) > d(n), where d(n) = number of divisors of n.

2, 4, 4, 6, 6, 12, 8, 12, 10, 12, 12, 24, 14, 16, 16, 18, 18, 24, 20, 24, 24, 24, 24, 36, 26, 28, 28, 30, 30, 36, 32, 36, 36, 36, 36, 48, 38, 40, 40, 48, 42, 48, 44, 48, 48, 48, 48, 60, 50, 54, 52, 54, 54, 60, 56, 60, 60, 60, 60, 120, 62, 63, 64, 66, 66, 72, 68, 70, 70

Offset: 1

Author

Leroy Quet, Mar 02 2008

Keywords

• nonn

Examples

			a(6)=12 because 6 has 4 divisors and the smallest integer > 6 which has more than 4 divisors is 12.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A112275.

Programs

Maple

with(numtheory): a:=proc (n) local m: for m from n+1 while tau(m) <= tau(n) do end do: m end proc: seq(a(n),n=1..60); # Emeric Deutsch, Mar 21 2008

Mathematica

a = {}; For[n = 1, n < 70, n++, i = n + 1; While[ ! DivisorSigma[0, i] > DivisorSigma[0, n], i++ ]; AppendTo[a, i]]; a (* Stefan Steinerberger, Mar 16 2008 *)
simd[n_]:=Module[{m=n+1,d=DivisorSigma[0,n]},While[DivisorSigma[0,m]<=d,m++];m]; Array[simd,70] (* Harvey P. Dale, Oct 03 2021 *)

Extensions

More terms from Stefan Steinerberger, Mar 16 2008