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A203662 Achilles number whose largest proper divisor is also an Achilles number.

%I A203662 #22 Sep 10 2024 19:38:27
%S A203662 864,1944,3888,4000,5400,6912,9000,10584,10800,10976,17496,18000,
%T A203662 21168,21600,24696,25000,26136,30375,31104,32000,34992,36000,36504,
%U A203662 42336,42592,43200,48600,49000,49392,50000,52272,55296,62208,62424,68600,69984
%N A203662 Achilles number whose largest proper divisor is also an Achilles number.
%C A203662 Exponent of smallest prime divisor of n is greater than or equal to 3.
%C A203662 Both N and the largest proper divisor of N share the same prime factors with different exponents.
%H A203662 Chai Wah Wu, <a href="/A203662/b203662.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Donovan Johnson)
%e A203662 17496 is in the sequence because 17496=2^3*3^7 (Achilles number) and the largest proper divisor 8748=2^2*3^7 is also an Achilles number.
%t A203662 (* First run the program for A052486 to define achillesQ *) Select[Range[50000], achillesQ[#] && achillesQ[Divisors[#][[-2]]] &] (* _Alonso del Arte_, Jan 05 2012 *)
%o A203662 (Python)
%o A203662 # uses program in A052486
%o A203662 from itertools import count, islice
%o A203662 from math import gcd
%o A203662 from sympy import factorint
%o A203662 def A203662_gen(): # generator of terms
%o A203662     def g(x):
%o A203662         (f:=factorint(x))[min(f)]-=1
%o A203662         return (x,f.values())
%o A203662     return map(lambda x:x[0],filter(lambda x:all(d>1 for d in x[1]) and gcd(*x[1])==1,map(g,(A052486(i) for i in count(1)))))
%o A203662 A203662_list = list(islice(A204662_gen(),20)) # _Chai Wah Wu_, Sep 10 2024
%Y A203662 Cf. A052486, A143610.
%K A203662 nonn
%O A203662 1,1
%A A203662 _Antonio Roldán_, Jan 04 2012