A392949 Numbers k such that sigma(k) = 2*k - 2*tau(phi(k)).

13, 22, 124, 1136, 1168, 1196, 1365, 564736, 4681792, 1086324608

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..10.

Example

k=13 has sigma(13) = 14, tau(phi(13)) = 6, 2*13 - 2*6 = 14.

Mathematica

q[k_] := DivisorSigma[1, k] == 2*k - 2*DivisorSigma[0, EulerPhi[k]]; Select[Range[600000], 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. A392950 (c=-1), A000396 (c=0), A392951 (c=1), A392952 (c=2).

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

Sequence in context: A164409 A301962 A298235 * A111676 A372056 A363482

Adjacent sequences: A392946 A392947 A392948 * A392950 A392951 A392952

Keyword

nonn,hard,more

Author

Aloe Poliszuk, Jan 27 2026

Status

approved