|
|
A064802
|
|
a(n) = Min { m > n | prime factorizations of m and n differ in one factor only}, a(1) = 1.
|
|
3
|
|
|
1, 3, 5, 6, 7, 9, 11, 12, 15, 14, 13, 18, 17, 21, 21, 24, 19, 27, 23, 28, 33, 26, 29, 36, 35, 34, 45, 42, 31, 42, 37, 48, 39, 38, 49, 54, 41, 46, 51, 56, 43, 63, 47, 52, 63, 58, 53, 72, 77, 70, 57, 68, 59, 81, 65, 84, 69, 62, 61, 84, 67, 74, 99, 96, 85, 78, 71, 76, 87, 98, 73
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
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
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|