A187086 Numbers n with property that sum of divisors of n except 1 and n is a positive square.
14, 39, 40, 46, 55, 94, 117, 130, 155, 158, 183, 190, 203, 208, 291, 292, 295, 299, 320, 323, 334, 430, 446, 475, 488, 530, 539, 549, 567, 579, 583, 638, 695, 718, 799, 873, 878, 890, 928, 943, 955, 959, 964, 979, 1030, 1118, 1191, 1255, 1384, 1411, 1454
Offset: 1
Keywords
Examples
divisors(14)={1,2,7,14}, 2+7=9=3^2 (= A187087(1));
divisors(40)={1,2,4,5,8,10,20,40}, 2+4+5+8+10+20=49=7^2 (= A187087(3)).
Links
- Zak Seidov, Table of n, a(n) for n = 1..1000
Programs
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Magma
IsA187086:=func< n | not IsPrime(n) and IsSquare(&+[ a: a in Divisors(n) | a ne 1 and a ne n ]) >; [ n: n in [2..2000] | IsA187086(n) ]; // Klaus Brockhaus, Mar 04 2011
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Maple
select(t -> not isprime(t) and issqr(numtheory:-sigma(t)-1-t), [$2..2000]); # Robert Israel, Oct 25 2017
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Mathematica
Select[Range@ 1500, And[! PrimeQ@ #, IntegerQ@ Sqrt[DivisorSigma[1, #] - # - 1]] &] (* Michael De Vlieger, Oct 25 2017 *)
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PARI
{for(n=1,2000,spf=sumdiv(n,x,x)-1-n;if(spf>0&&issquare(spf),print1(n", ")))}
Comments