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

1,1

Comments

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

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 *)

Crossrefs

Cf. A079427, A112276.

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

Sequence in context: A134361 A142727 A347388 * A335876 A306974 A278400

Adjacent sequences: A112272 A112273 A112274 * A112276 A112277 A112278

Keyword

nonn

Author

Reinhard Zumkeller, Sep 01 2005

Status

approved