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

60, 5472, 2500704, 24361213461200, 808989640739424

Offset

1,1

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

Links

Table of n, a(n) for n=1..5.

Example

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

Mathematica

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

Prog

(Magma) [m: m in [1..10^7] | SumOfDivisors(m) - 2*m eq m - NumberOfDivisors(m)];
(PARI) isok(m) = my(f=factor(m)); sigma(f) + numdiv(m) == 3*m; \\ Michel Marcus, Nov 13 2019

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)).

Sequence in context: A084274 A289307 A091032 * A178785 A091753 A336629

Adjacent sequences: A328948 A328949 A328950 * A328952 A328953 A328954

Keyword

nonn,more

Author

Jaroslav Krizek, Nov 10 2019

Extensions

a(4) from Martin Ehrenstein, Jul 25 2023

a(5) from Jud McCranie, Jan 21 2026

Status

approved