A396264 Numbers j such that Sum_{d|j, d < j} (-1)^d * d is equal to j.

60, 728, 60512

Offset

1,1

Comments

Also includes 1099176108032, 288229001763749888.

Numbers k such that A058344(k) = -k.

a(4) > 10^10. - Amiram Eldar, May 22 2026

Links

Table of n, a(n) for n=1..3.

Example

60 is a term since 60 has 11 proper divisors {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30} and -1 + 2 - 3 + 4 - 5 + 6 + 10 + 12 - 15 + 20 + 30 = 60.

Mathematica

f[p_, e_] := If[p == 2, 3 - 2^(e + 1), (p^(e + 1) - 1)/(p - 1)]; q[1] = False; q[k_] := Times @@ f @@@ FactorInteger[k] == k*(-(-1)^k - 1); Select[Range[10^5], q] (* Amiram Eldar, May 20 2026 *)

Prog

(PARI) isok(k) = {my(f = factor(k)); prod(i = 1, #f~, if(f[i, 1] == 2, 3 - 2^(f[i, 2] + 1), (f[i, 1]^(f[i, 2] + 1) - 1)/(f[i, 1] - 1))) == k*(-(-1)^k - 1); } \\ Amiram Eldar, May 20 2026

Crossrefs

Cf. A000396, A002129, A058344, A348583.

Sequence in context: A138409 A024016 A348583 * A349871 A112042 A168307

Adjacent sequences: A396261 A396262 A396263 * A396265 A396266 A396267

Keyword

nonn,more,bref

Author

Ilya Gutkovskiy, May 20 2026

Status

approved