A206367 (2,3)-imperfect numbers.

3, 15, 18, 36, 72, 255, 1152, 2709, 65535, 294912, 4294967295, 4380480000

Offset: 1

Author

N. J. A. Sloane, Feb 06 2012

Keywords

• nonn
• more

Comments

a(13) > 10^10, if it exists. - Amiram Eldar, Sep 12 2023

Links

• László Tóth, A survey of the alternating sum-of-divisors function, arXiv:1111.4842 [math.NT], 2011-2014. See p. 7.

Crossrefs

Cf. A127725 (2-imperfect).

Cf. A206369 (beta).

Programs

Mathematica

f[p_, e_] := ((-1)^e + p^(e + 1))/(p + 1); s[n_] := Times @@ f @@@ FactorInteger[n]; s[1] = 1; Select[Range[300000], # == 3 * s[s[#]] &] (* Amiram Eldar, Sep 12 2023 *)

PARI

beta(n) = sumdiv(n, d, d*(-1)^bigomega(n/d));
isok(k) = 3*beta(beta(k)) == k; \\ Michel Marcus, Sep 11 2023

Extensions

a(7)-a(10) from Michel Marcus, Sep 11 2023

a(11)-a(12) from Amiram Eldar, Sep 12 2023