A328951 Numbers m such that sigma(m) + tau(m) = 3m.

60, 5472, 2500704, 24361213461200

Offset: 1

Author

Jaroslav Krizek, Nov 10 2019

Keywords

• nonn
• more

Comments

Abundant numbers m with abundance A(m) = m - tau(m) = A049820(m), where A049820(n) is the number of non-divisors of n.

Subsequence of A056076.

Corresponding values of A(m) = m - tau(m): 48, 5436, 2500632, ...

4 is the only number m with deficiency D(m) = m - tau(m).

808989640739424 is also a term. - Giovanni Resta, Nov 14 2019

Examples

			60 is a term because sigma(60) + tau(60) = 3*60; 168 + 12 = 180 = 3*60.
		

Crossrefs

Cf. A000005, A000203, A033880, A049820, A056076.

Cf. A083874 (numbers m such that sigma(m) + tau(m) = 2m).

Cf. A011251 (numbers m such that sigma(m) + phi(m) = 3m).

Cf. A329104 (numbers m with abundance A(m) = tau(m)).

Programs

Magma

[m: m in [1..10^7] | SumOfDivisors(m) - 2*m eq m - NumberOfDivisors(m)];

Mathematica

Select[Range[3*10^6], DivisorSigma[0, #] + DivisorSigma[1, #] == 3# &] (* Amiram Eldar, Nov 10 2019 *)

PARI

isok(m) = my(f=factor(m)); sigma(f) + numdiv(m) == 3*m; \\ Michel Marcus, Nov 13 2019

Extensions

a(4) from Martin Ehrenstein, Jul 25 2023