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URL: https://oeis.org/A228957

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A228957
Numbers n such that n/rad(n) is greater than the greatest prime dividing n.
2
8, 16, 24, 27, 32, 36, 48, 54, 64, 72, 80, 81, 96, 100, 108, 112, 125, 128, 135, 144, 160, 162, 180, 189, 192, 196, 200, 216, 224, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 336, 343, 352, 360, 375, 378, 384, 392, 400, 405, 416, 432, 441, 448, 450, 480
OFFSET
1,1
COMMENTS
n such that n/rad(n)> gpf(n); numbers n such that n/A007947(n) > A006530(n) where A007947 is the product of the distinct prime factors of n and A006530 is the greatest prime dividing n.
The sequence A137845 (logarithmically smooth numbers)is included in this sequence.
It appears that there exists consecutive numbers such that (80,81), (224,225), (675,676), (1088,1089), (1215,1216), (2375,2376), (2400,2401), (2600, 2601), (3024,3025), (3249,3250), (3968,3969), (4224,4225), (4374,4375), (5831,5832),...
But it appears also that (2400,2401) and (4374,4375) are the only consecutive numbers in the sequence A137845.
LINKS
EXAMPLE
24 is in the sequence because the prime divisors of 24 are 2 and 3 and 24/2*3 > 3.
MAPLE
with(numtheory) :for n from 1 to 400 do:x:=factorset(n):n1:=nops(x): p:= product('x[i]', 'i'=1..n1):m:=n/p:if m> x[n1]then printf(`%d, `, n):else fi:od:
MATHEMATICA
rad[n_]:=Times@@(First@#&/@FactorInteger@n); Select[Range[2, 1000], FactorInteger[#][[-1, 1]]<#/rad[#]&]
nrQ[n_]:=Module[{x=FactorInteger[n][[All, 1]]}, n/Times@@x>Last[x]]; Select[Range[ 500], nrQ] (* Harvey P. Dale, Jun 15 2022 *)
PROG
(PARI) is(n)=my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]-1)) > f[#f~, 1] \\ Charles R Greathouse IV, Sep 09 2013
CROSSREFS
A366250 is a subsequence.
Sequence in context: A078130 A062171 A048108 * A137845 A046099 A375145
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 09 2013
STATUS
approved