A329104 Numbers m such that sigma(m) - tau(m) = 2m.

56, 7192, 7232, 7912, 10792, 17272, 30592, 114256, 2154584, 3428368, 89245784

Offset: 1

Author

Jaroslav Krizek, Nov 04 2019

Keywords

• nonn
• more

Comments

Abundant numbers m with abundance A(m) = tau(m).

Corresponding values of A(m) = tau(m): 8, 16, 14, 16, 16, 16, 16, 20, 32, 30, 32, ...

a(12) > 10^13, if it exists. - Giovanni Resta, Nov 07 2019

Examples

			Number 56 is in the sequence because sigma(56) - tau(56) = 2*56; 120 - 8 = 112.
		

Crossrefs

Cf. A000005, A000203, A033880, A065608.

Cf. A083874 (deficient numbers m with deficiency D(m) = tau(m)).

Programs

Magma

[m: m in [1..10^5] | SumOfDivisors(m) - NumberOfDivisors(m) eq 2*m];

Mathematica

Select[Range[4*10^6], DivisorSigma[1, #] - DivisorSigma[0, #] == 2 # &] (* Amiram Eldar, Nov 04 2019 *)

PARI

isok(m) = my(f=factor(m)); sigma(f) - numdiv(f) == 2*m; \\ Michel Marcus, Nov 05 2019

Extensions

a(11) from Amiram Eldar, Nov 04 2019