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

1,1

Comments

Or, Chowla's function of n is a positive square.

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

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)).

Maple

select(t -> not isprime(t) and issqr(numtheory:-sigma(t)-1-t), [$2..2000]); # Robert Israel, Oct 25 2017

Mathematica

Select[Range@ 1500, And[! PrimeQ@ #, IntegerQ@ Sqrt[DivisorSigma[1, #] - # - 1]] &] (* Michael De Vlieger, Oct 25 2017 *)

Prog

(PARI) {for(n=1, 2000, spf=sumdiv(n, x, x)-1-n; if(spf>0&&issquare(spf), print1(n", ")))}
(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

Crossrefs

Cf. A048050, A187087.

Sequence in context: A231391 A231459 A244702 * A044091 A044472 A178564

Adjacent sequences: A187083 A187084 A187085 * A187087 A187088 A187089

Keyword

nonn

Author

Zak Seidov, Mar 04 2011

Status

approved