OFFSET
1,2
COMMENTS
A094457 gives next smaller comparable number, replacing the prime factor 2 with 1. - Michael De Vlieger, Jan 31 2015
From Peter Munn, Oct 13 2023: (Start)
For n > 1, a(n) is the smallest number m > n in the factorization neighborhood of n given by A127185(m, n) <= 2.
Usually, the minimum m is achieved by replacing the largest prime factor with the next prime. So through the first 60 terms about 1 term in 5 differs from the corresponding term of A253550, but this proportion drops to 611 of the first 10000 terms. Nevertheless, I see reasons (deriving from the distribution of the lengths of prime gaps) to doubt that the asymptotic density of {n : a(n) <> A253550(n)} is less than 611/10000.
(End)
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
EXAMPLE
n = 20 = 2 * 2 * 5: as 2 * 3 * 5 > 2 * 2 * 7 = 28 we have a(20) = 28.
MATHEMATICA
f[n_] := Block[{g}, g[x_] := Flatten[Table[#1, {#2}] & @@@ FactorInteger@ x]; If[n == 1, 1, Min[Times @@ MapAt[NextPrime, g[n], #] & /@ Range[Length@ g[n]]]]]; Array[f, 71] (* Michael De Vlieger, Jan 31 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Oct 21 2001
STATUS
approved