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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 27 12:27 EDT 2020. Contains 334657 sequences. (Running on oeis4.)