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

60, 5472, 2500704, 24361213461200, 808989640739424, 568521310483526688

Offset

1,1

Comments

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

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

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

Links

Table of n, a(n) for n=1..6.

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

Subsequence of A056076.

Cf. A000005, A000203, A033880, A049820.

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,changed

Author

Jaroslav Krizek, Nov 10 2019

Extensions

a(4) from Martin Ehrenstein, Jul 25 2023

a(5) from Giovanni Resta confirmed and added by Jud McCranie, Jan 21 2026

a(6) from Max Alekseyev, Jun 24 2026

Status

approved