A392507 - OEIS

%I #22 Jan 26 2026 11:35:20

%S 1,12,90,2878,3118,3595,3949,4063,4117,4183,4187,4189,4279,4427,18716,

%T 19653,24323,25093,25813,25853,63984,156664,163190,171346,183585,

%U 187634,191666,192826,193234,193486,194438,194578,208029,209247,212889,216471,217047,217857,218697

%N Numbers k such that the abundancy index of sigma(k) divided by the abundancy index of d(k) equals a whole number.

%C Includes the sublime numbers.

%H Robert G. Wilson v, <a href="/A392507/b392507.txt">Table of n, a(n) for n = 1..3879</a>

%e 12 has sigma(12) = 28, and d(12) = 6, and sigma(28)/28 = 2 and sigma(6)/6 = 2, thus 2/2 = 1.

%e 4117 has sigma(4117) = 4320, and d(4117) = 4, and sigma(4320)/4320 = 7/2 and sigma(4)/4 = 7/4 and 7/2 divided by 7/4 is 2.

%t fQ[n_] := IntegerQ[ Divide @@ DivisorSigma[-1, DivisorSigma[{1, 0}, n]]]; Select[Range[220000], fQ] (* _Amiram Eldar_, Jan 14 2026 *) (* slightly modified by _Robert G. Wilson v_, Jan 25 2026 for speed *)

%o (PARI) isok(k) = denominator(sigma(sigma(k),-1)/sigma(numdiv(k),-1)) == 1; \\ _Michel Marcus_, Jan 15 2026

%Y Cf. A081357, A000203, A000005.

%Y Cf. A392506 (a subsequence).

%K nonn

%O 1,2

%A _Leo Hennig_, Jan 14 2026

%E More terms from _Amiram Eldar_, Jan 14 2026