A392950 - OEIS

%I #11 Feb 02 2026 21:17:05

%S 1,2,3,14,184,248,6490,35595,125476,407524,13228352,33763328,99413968,

%T 223449568,500860912,3602922208

%N Numbers k such that sigma(k) = 2*k - tau(phi(k)).

%C Also numbers k with abundance -tau(phi(k)).

%e k=14 has sigma(14) = 24, tau(phi(14)) = 4, 2*14 - 4 = 24.

%e k=184 has sigma(184) = 360, tau(phi(184)) = 8, 2*184 - 8 = 360.

%t q[k_] := DivisorSigma[1, k] == 2*k - DivisorSigma[0, EulerPhi[k]]; Select[Range[500000], q] (* _Amiram Eldar_, Jan 28 2026 *)

%o (PARI) isok(n) = my(f=factorint(n)); sigma(f) == 2*n - numdiv(eulerphi(f));

%Y If we generalize to numbers x with abundance c*tau(phi(x)), then a(n) is the case of c=-1, and we have:

%Y Cf. A392949 (c=-2), A000396 (c=0), A392951 (c=1), A392952 (c=2).

%Y Cf. A000005 (tau), A000010 (phi), A000203 (sigma), A005843, A301975.

%K nonn,hard,more

%O 1,2

%A _Aloe Poliszuk_, Jan 27 2026