Infinitary superperfect numbers. (English) Zbl 1399.11018
Summary: We show that 9 is the only odd infinitary superperfect number. For the definition see [G. L. Cohen, Math. Comput. 43, 395–411 (1990; Zbl 0689.10014)].
For an addendum and corrigenda see [ibid. 48, 199–201 (2018; Zbl 1424.11012).
For an addendum and corrigenda see [ibid. 48, 199–201 (2018; Zbl 1424.11012).
MSC:
| 11A25 | Arithmetic functions; related numbers; inversion formulas |
Keywords:
odd perfect numbers; infinitary superperfect numbers; unitary divisors; infinitary divisors; sum of divisorsOnline Encyclopedia of Integer Sequences:
a(n) = isigma(n): sum of infinitary divisors of n.Numbers m such that A049417(A049417(m)) = k*m for some k where A049417 is the infinitary sigma function.
a(n) is the least k such that A049417(A049417(k)) = n*k, where A049417 is the infinitary sigma function, or 0 if no such k exists.
