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

1,1

Links

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

Example

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

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 *)

Crossrefs

Cf. A000005, A112275.

Sequence in context: A226951 A251557 A231901 * A153494 A352749 A205404

Adjacent sequences: A135971 A135972 A135973 * A135975 A135976 A135977

Keyword

nonn

Author

Leroy Quet, Mar 02 2008

Extensions

More terms from Stefan Steinerberger, Mar 16 2008

Status

approved