A329104 - OEIS

%I #18 Aug 28 2024 14:58:28

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

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

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

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

%C a(12) > 10^13, if it exists. - _Giovanni Resta_, Nov 07 2019

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

%t Select[Range[4*10^6], DivisorSigma[1, #] - DivisorSigma[0, #] == 2 # &] (* _Amiram Eldar_, Nov 04 2019 *)

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

%o (PARI) isok(m) = my(f=factor(m)); sigma(f) - numdiv(f) == 2*m; \\ _Michel Marcus_, Nov 05 2019

%Y Cf. A000005, A000203, A033880, A065608.

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

%K nonn,more

%O 1,1

%A _Jaroslav Krizek_, Nov 04 2019

%E a(11) from _Amiram Eldar_, Nov 04 2019