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A112275
Smallest number greater than n having at least as many divisors as n.
4
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
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. A138171 (odd n for which a(n) > n+1).
Sequence in context: A134361 A142727 A347388 * A335876 A306974 A278400
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 01 2005
STATUS
approved