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A206367
(2,3)-imperfect numbers.
1
3, 15, 18, 36, 72, 255, 1152, 2709, 65535, 294912, 4294967295, 4380480000
OFFSET
1,1
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.
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 *)
PROG
(PARI) beta(n) = sumdiv(n, d, d*(-1)^bigomega(n/d));
isok(k) = 3*beta(beta(k)) == k; \\ Michel Marcus, Sep 11 2023
CROSSREFS
Cf. A127725 (2-imperfect).
Cf. A206369 (beta).
Sequence in context: A039559 A045753 A022381 * A039570 A032644 A124877
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Feb 06 2012
EXTENSIONS
a(7)-a(10) from Michel Marcus, Sep 11 2023
a(11)-a(12) from Amiram Eldar, Sep 12 2023
STATUS
approved