A112275 Smallest number greater than n having at least as many divisors as n.

2, 3, 4, 6, 6, 8, 8, 10, 10, 12, 12, 18, 14, 15, 16, 18, 18, 20, 20, 24, 22, 24, 24, 30, 26, 27, 28, 30, 30, 36, 32, 36, 34, 35, 36, 48, 38, 39, 40, 42, 42, 48, 44, 45, 48, 48, 48, 60, 50, 52, 52, 54, 54, 56, 56, 60, 58, 60, 60, 72, 62, 63, 64, 66, 66, 70, 68, 70, 70, 72, 72, 84

Offset: 1

Author

Reinhard Zumkeller, Sep 01 2005

Keywords

• nonn

Comments

A000005(n) <= A000005(a(n)) and A000005(k) < A000005(n) for n

A000005(2*k-1) <= A000005(2*k) for 1<=k<=22. - Corrected by Robert Israel, Jul 23 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A079427, A112276.

Cf. A138171 (odd n for which a(n) > n+1).

Programs

Maple

N:= 1000: # for all terms before the first term > N
taus:= map(numtheory:-tau,[$1..N]):
for n from 1 to N do
found:= false:
for k from n+1 to N while not found do
   if taus[k]>=taus[n] then found:= true; A[n]:= k fi
od;
if not found then break fi
od:
seq(A[i],i=1..n-1); # Robert Israel, Jul 23 2019

Mathematica

kmax[n_] := 2 n;
a[n_] := Module[{tau = DivisorSigma[0, n], k},
     For[k = n + 1, k <= kmax[n], k++,
          If[DivisorSigma[0, k] >= tau, Return[k]]];
     Print["a(n) = k not found for n = ", n]];
Array[a, 100] (* Jean-François Alcover, Dec 15 2021 *)

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