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A328951
Numbers m such that sigma(m) + tau(m) = 3m.
0
60, 5472, 2500704, 24361213461200
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
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. 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
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Nov 10 2019
EXTENSIONS
a(4) from Martin Ehrenstein, Jul 25 2023
STATUS
approved