A206367 - OEIS

%I #19 Sep 12 2023 04:39:32

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

%N (2,3)-imperfect numbers.

%C a(13) > 10^10, if it exists. - _Amiram Eldar_, Sep 12 2023

%H László Tóth, <a href="http://arxiv.org/abs/1111.4842">A survey of the alternating sum-of-divisors function</a>, arXiv:1111.4842 [math.NT], 2011-2014. See p. 7.

%t 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 *)

%o (PARI) beta(n) = sumdiv(n, d, d*(-1)^bigomega(n/d));

%o isok(k) = 3*beta(beta(k)) == k; \\ _Michel Marcus_, Sep 11 2023

%Y Cf. A127725 (2-imperfect).

%Y Cf. A206369 (beta).

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Feb 06 2012

%E a(7)-a(10) from _Michel Marcus_, Sep 11 2023

%E a(11)-a(12) from _Amiram Eldar_, Sep 12 2023