A099650 -id:A099650 - cp's OEIS frontend

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

Paolo P. Lava, Aug 09 2017

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

Cf. A000005, A099650, A111592, A290704.

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);

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

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

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

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

A290704 Solutions to 2*x - phi(x) = sigma(x)/2, where phi(x) is the Euler totient function of x.

Original entry on oeis.org

1680, 4200, 27000, 175392, 282960, 707400, 1668480, 3344544, 5658480, 14146200, 48644064, 90008880, 130110624, 225022200, 357994728, 460763160, 607281696, 1926458352, 3830537880, 5857651296, 7840881216, 8414628480, 8704032876, 8843224500, 14279194512, 29522053080

Offset: 1

Paolo P. Lava, Aug 09 2017

nonn

			phi(1680) = 384, sigma(1680) = 5952 and 2*1680 - 384 = 2976 = 5952/2.

Like A099650 but with totient phi(x) replaced by cototient x - phi(x).

Cf. A000010, A051953, A099650, A111592, A290703.

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

a(10)-a(26) from Giovanni Resta, Aug 25 2017

cp's OEIS Frontend

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

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