

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
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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

Michel Lagneau, Table of n, a(n) for n = 1..10000


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[#]&]


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

Cf. A006530, A007947, A137845.
Sequence in context: A078130 A062171 A048108 * A137845 A046099 A033859
Adjacent sequences: A228954 A228955 A228956 * A228958 A228959 A228960


KEYWORD

nonn


AUTHOR

Michel Lagneau, Sep 09 2013


STATUS

approved



