A392951 Numbers k such that sigma(k) = 2*k + tau(phi(k)).

56, 186, 222, 258, 402, 426, 474, 606, 618, 678, 786, 834, 1146, 1182, 1338, 1434, 1506, 1698, 1866, 2202, 2514, 2586, 2634, 2658, 2994, 3558, 3594, 3642, 3714, 3858, 3882, 3954, 4062, 4098, 4458, 4722, 4938, 4962, 5442, 5682, 5826, 5862, 6186, 6234

Offset

1,1

Comments

Also numbers k with abundance tau(phi(k)).

Links

Aloe Poliszuk, Table of n, a(n) for n = 1..10000

Example

k=56 has sigma(56) = 120, tau(phi(56)) = 8, 2*56 + 8 = 120.

Mathematica

q[k_] := DivisorSigma[1, k] == 2*k + DivisorSigma[0, EulerPhi[k]]; Select[Range[6500], q] (* Amiram Eldar, Jan 28 2026 *)

Prog

(PARI) isok(n) = my(f=factorint(n)); sigma(f) == 2*n + numdiv(eulerphi(f));

Crossrefs

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

Cf. A392949 (c=-2), A392950 (c=-1), A000396 (c=0), A392952 (c=2).

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

Sequence in context: A115620 A224108 A234114 * A234107 A389855 A136547

Adjacent sequences: A392948 A392949 A392950 * A392952 A392953 A392954

Keyword

nonn

Author

Aloe Poliszuk, Jan 27 2026

Status

approved