A392952 Numbers k such that sigma(k) = 2*k + 2*tau(phi(k)).

40, 42, 54, 66, 102, 138, 176, 282, 354, 498, 642, 1002, 1074, 1362, 1578, 2082, 2154, 2298, 2802, 2874, 3018, 3164, 3378, 3522, 4314, 4544, 4672, 5034, 5178, 5322, 5898, 6114, 7122, 7698, 7842, 7914, 8202, 8634, 8922, 9138, 9714, 10938, 11442, 12162

Offset

1,1

Comments

Also numbers k with abundance 2 * tau(phi(k)).

Links

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

Example

k=40 has sigma(40) = 90, tau(phi(40)) = 5, 2*40 + 2*5 = 90.
k=102 has sigma(102) = 216, tau(phi(102)) = 6, 2*102 + 2*6 = 216.

Mathematica

q[k_] := DivisorSigma[1, k] == 2*k + 2*DivisorSigma[0, EulerPhi[k]]; Select[Range[13000], 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=2, and we have:

Cf. A392949 (c=-2), A392950 (c=-1), A000396 (c=0), A392951 (c=1).

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

Sequence in context: A214563 A111167 A378652 * A070980 A131535 A118473

Adjacent sequences: A392949 A392950 A392951 * A392953 A392954 A392955

Keyword

nonn

Author

Aloe Poliszuk, Jan 27 2026

Status

approved