A385148 a(n) = A001065(A346878(n)).

0, 1, 6, 1, 7, 15, 8, 9, 11, 14, 10, 55, 15, 28, 54, 1, 22, 17, 14, 43, 66, 50, 16, 64, 1, 26, 78, 63, 31, 172, 20, 41, 90, 32, 40, 45, 50, 63, 144, 56, 40, 196, 26, 76, 259, 64, 43, 236, 1, 65, 126, 56, 64, 136, 56, 134, 186, 50, 34, 504, 63, 117, 198, 1, 64, 300, 74, 70, 222, 203

Offset

1,3

Comments

There are only 2 known fixed points 26 and 296; they are the numbers k such that k = sigma(m) - m where m = sigma(2*k) - 2*k as investigated by S. I. Dimitrov. See link.

Links

Table of n, a(n) for n=1..70.

S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024. See Table 2 p. 7.

Mathematica

f[x_] := DivisorSigma[1, x] - x; Table[Nest[f, 2*n, 2], {n, 120}] (* Michael De Vlieger, Jun 19 2025 *)

Prog

(PARI) a(n) = my(m=sigma(2*n) - 2*n); sigma(m) - m ;

Crossrefs

Cf. A001065, A346878.

Cf. A377766 (twice the integers that satisfy a(n)=1).

Cf. A384411.

Sequence in context: A261622 A397006 A046902 * A204205 A143019 A337369

Adjacent sequences: A385145 A385146 A385147 * A385149 A385150 A385151

Keyword

nonn

Author

Michel Marcus, Jun 19 2025

Status

approved