cp's OEIS Frontend

A187086 Numbers n with property that sum of divisors of n except 1 and n is a positive square.

%I A187086 #22 Sep 08 2022 08:45:56
%S A187086 14,39,40,46,55,94,117,130,155,158,183,190,203,208,291,292,295,299,
%T A187086 320,323,334,430,446,475,488,530,539,549,567,579,583,638,695,718,799,
%U A187086 873,878,890,928,943,955,959,964,979,1030,1118,1191,1255,1384,1411,1454
%N A187086 Numbers n with property that sum of divisors of n except 1 and n is a positive square.
%C A187086 Or, Chowla's function of n is a positive square.
%H A187086 Zak Seidov, <a href="/A187086/b187086.txt">Table of n, a(n) for n = 1..1000</a>
%e A187086 divisors(14)={1,2,7,14}, 2+7=9=3^2 (= A187087(1));
%e A187086 divisors(40)={1,2,4,5,8,10,20,40}, 2+4+5+8+10+20=49=7^2 (= A187087(3)).
%p A187086 select(t -> not isprime(t) and issqr(numtheory:-sigma(t)-1-t), [$2..2000]); # _Robert Israel_, Oct 25 2017
%t A187086 Select[Range@ 1500, And[! PrimeQ@ #, IntegerQ@ Sqrt[DivisorSigma[1, #] - # - 1]] &] (* _Michael De Vlieger_, Oct 25 2017 *)
%o A187086 (PARI) {for(n=1,2000,spf=sumdiv(n,x,x)-1-n;if(spf>0&&issquare(spf),print1(n", ")))}
%o A187086 (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
%Y A187086 Cf. A048050, A187087.
%K A187086 nonn
%O A187086 1,1
%A A187086 _Zak Seidov_, Mar 04 2011