A290703 Solutions to x + d(x) = sigma(x)/2, where d(x) is the number of divisors of x.

176, 2205, 7544, 10184, 28544, 503296, 1020568, 2051072, 6019264, 10001848, 15317696, 35019968, 354375344, 535871488, 9175990784, 115917884416

Offset: 1

Author

Paolo P. Lava, Aug 09 2017

Keywords

• nonn
• more

Examples

			d(176) = 10, sigma(176) = 372 and 176 + 10 = 186 = 372/2.
		

Crossrefs

Cf. A000005, A099650, A111592, A290704.

Programs

Maple

with(numtheory): P:=proc(q) local n; for n from 1 to q do if
n+tau(n)=sigma(n)/2 then print(n); fi; od; end: P(10^9);

Mathematica

Select[Range[10^7], # + DivisorSigma[0, #] == DivisorSigma[1, #]/2 &] (* Michael De Vlieger, Aug 26 2017 *)

PARI

isok(x) = x + numdiv(x) == sigma(x)/2; \\ Michel Marcus, Aug 25 2017

Extensions

a(11)-a(12) from Michel Marcus, Aug 25 2017

a(13)-a(16) from Giovanni Resta, Aug 25 2017