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%I #14 Feb 13 2015 00:25:49
%S 300,37026,81900,3719430,60960900,746876130,37456118700,1371798057630,
%T 45093761813100,1750692518344770,72411562719475980,
%U 4075432279946977950,430815330651894087900
%N a(n) is the smallest number k having n prime distinct divisors such that k is divisible by the square of the sum of its prime divisors.
%C n > = 3, because if n = 2 then k = p^a * q^b, where p and q are distinct primes and (p+q)^2 | k => p+q ==0 (mod p) or 0 (mod (q), but p==0 (mod q) and q==0 (mod p) are impossible.
%H Charles R Greathouse IV, <a href="/A190880/a190880.gp.txt">GP script for computing terms</a>
%e a(4) = 37026 because the prime distinct divisors of this number are {2, 3, 11, 17}, (2 + 3 + 11 + 17)^2 = 1089, and 37026 = 1089*34.
%p with(numtheory):for n from 3 to 10 do:id:=0:for k from 1 to 5000000 while(id=0)
%p do:x:=factorset(k):n1:=nops(x):s:=0:for p from 1 to n1 do: s:=s+x[p]:od:s:=s^2:if
%p n1= n and irem(k,s)=0 then id:=1:printf ( "%d %d \n",n, k):else fi:od:od:
%o (PARI) \\ See links for script.
%Y Cf. A190879.
%K nonn,hard
%O 3,1
%A _Michel Lagneau_, May 23 2011
%E a(8)-a(13) from _Charles R Greathouse IV_, May 23 2011
%E a(14)-a(15) from _Charles R Greathouse IV_, May 24 2011
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