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A225882 Numbers n such that core(n) is equal to the sum of the proper square divisors of n, where core(n) = A007913(n). 3

%I

%S 20,90,336,650,5440,7371,13000,14762,28730,30240,83810,87296,130682,

%T 147420,218400,280370,295240,406875,708122,924482,1397760,1875530,

%U 2613640,3536000,4881890,4960032,5884851,7856640,7893290,8137500

%N Numbers n such that core(n) is equal to the sum of the proper square divisors of n, where core(n) = A007913(n).

%C If p is prime and p^2+1 squarefree, then p^2*(p^2+1) is in the sequence.

%H Charles R Greathouse IV and Giovanni Resta, <a href="/A225882/b225882.txt">Table of n, a(n) for n = 1..282</a> (terms < 5*10^11. First 80 terms from Charles R Greathouse IV)

%e 13000 is a term because core(13000) = 130 = 100 + 25 + 4 + 1.

%o (PARI)

%o for(n=2,10^8,if(core(n)==sumdiv(n,d,d*issquare(d)),print(n)))

%o (PARI) ssd(f)=prod(i=1,#f[,1],(f[i,1]^(f[i,2]+2-f[i,2]%2)-1)/(f[i,1]^2-1))

%o is(n)=my(f=factor(n));prod(i=1,#f[,1],f[i,1]^(f[i,2]%2))==ssd(f) && n>1 \\ _Charles R Greathouse IV_, May 20 2013

%Y Cf. A007913, A035316, A225880, A225881.

%K nonn

%O 1,1

%A _Antonio Roldán_, May 19 2013

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Last modified October 15 11:03 EDT 2018. Contains 316224 sequences. (Running on oeis4.)