A258101 Number x such that usigma(x) = (-1)sigma(x), where usigma(x) is the sum of unitary divisors of x (A034448) and (-1)sigma(x) is defined in A049060 .

1, 4, 15867, 21357, 49887, 63468, 69875, 85428, 86387, 149875, 199548, 247475, 271607, 279500, 293944, 318681, 345548, 599500, 637659, 989900, 1086428, 1169091, 1274724, 1897875, 1913571, 2550636, 2665269, 2801880, 2855691

Offset: 1

Author

Paolo P. Lava, May 20 2015

Keywords

• nonn

Examples

			usigma(1) = (-1)sigma(1) = 1;
usigma(4) =  (-1)sigma(4) = 5;
usigma(15867) = (-1)sigma(15867) = 18480; etc.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A034448, A049060, A258106.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,d,k,n;
a:=0; for n from 1 to q do a:=divisors(n); d:=0; for k from 1 to nops(a)
do if gcd(a[k],n/a[k])=1 then d:=d+a[k]; fi; od; a:=ifactors(n)[2]; b:=1;
for k from 1 to nops(a) do b:=b*(-1+sum(a[k][1]^j,j=1..a[k][2])); od;
if b=d then print(n); fi; od; end: P(10^9);

Mathematica

aQ[n_] := Module[{f = FactorInteger[n]}, p = f[[;;,1]]; e = f[[;;,2]]; Times@@(p^e+1) == Times@@((p^(e+1)-2*p+1)/(p-1))]; Join[{1}, Select[Range[2, 200000 ], aQ]] (* Amiram Eldar, Jun 23 2019 *)