A351048 Numbers k such that tau(k) | k'.

1, 8, 9, 15, 20, 35, 39, 44, 51, 55, 68, 72, 87, 91, 92, 95, 108, 111, 112, 115, 116, 119, 123, 128, 143, 155, 159, 160, 164, 183, 187, 188, 189, 196, 203, 212, 215, 219, 235, 236, 247, 259, 267, 272, 284, 287, 291, 295, 299, 303, 319, 323, 327, 332, 335, 339, 352, 355, 356

Offset

1,2

Comments

Numbers k such that A000005(k) divides A003415(k).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

39 is in the sequence since tau(39) = 4 | 16 = 39'.

Maple

filter:= proc(n) local F, t;
F:= ifactors(n)[2];
  (n * add(t[2]/t[1], t=F)) mod mul(t[2]+1, t=F) = 0
end proc:
select(filter, [$1..1000]); # Robert Israel, May 05 2024

Mathematica

q[1] = True; q[n_] := Module[{f = FactorInteger[n]}, Divisible[n * Plus @@ ((Last[#]/First[#]) & /@ f), Times @@ (1 + Last[#] & /@ f)]]; Select[Range[350], q] (* Amiram Eldar, Feb 03 2022 *)

Crossrefs

Cf. A000005 (tau), A003415 (arithmetic derivative), A351163. Contains A080774.

Sequence in context: A256351 A050688 A134334 * A292188 A301659 A265221

Adjacent sequences: A351045 A351046 A351047 * A351049 A351050 A351051

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 03 2022

Status

approved