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A203662
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Achilles number whose largest proper divisor is also an Achilles number.
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2
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864, 1944, 3888, 4000, 5400, 6912, 9000, 10584, 10800, 10976, 17496, 18000, 21168, 21600, 24696, 25000, 26136, 30375, 31104, 32000, 34992, 36000, 36504, 42336, 42592, 43200, 48600, 49000, 49392, 50000, 52272, 55296, 62208, 62424, 68600, 69984
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OFFSET
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1,1
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COMMENTS
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Exponent of smallest prime divisor of n is greater than or equal to 3.
Both N and the largest proper divisor of N share the same prime factors with different exponents.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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(* First run the program for A052486 to define achillesQ *) Select[Range[50000], achillesQ[#] && achillesQ[Divisors[#][[-2]]] &] (* Alonso del Arte, Jan 05 2012 *)
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PROG
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(Python)
from itertools import count, islice
from math import gcd
from sympy import factorint
def A203662_gen(): # generator of terms
def g(x):
(f:=factorint(x))[min(f)]-=1
return (x, f.values())
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)))))
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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