A392950 Numbers k such that sigma(k) = 2*k - tau(phi(k)).

1, 2, 3, 14, 184, 248, 6490, 35595, 125476, 407524, 13228352, 33763328, 99413968, 223449568, 500860912, 3602922208

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..16.

Example

k=14 has sigma(14) = 24, tau(phi(14)) = 4, 2*14 - 4 = 24.
k=184 has sigma(184) = 360, tau(phi(184)) = 8, 2*184 - 8 = 360.

Mathematica

q[k_] := DivisorSigma[1, k] == 2*k - DivisorSigma[0, EulerPhi[k]]; Select[Range[500000], 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), A000396 (c=0), A392951 (c=1), A392952 (c=2).

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

Sequence in context: A006279 A041521 A101003 * A042071 A042817 A224848

Adjacent sequences: A392947 A392948 A392949 * A392951 A392952 A392953

Keyword

nonn,hard,more

Author

Aloe Poliszuk, Jan 27 2026

Status

approved