A351163 Numbers k' / tau(k) such that tau(k) | k'.

0, 3, 2, 2, 4, 3, 4, 8, 5, 4, 12, 13, 8, 5, 16, 6, 18, 10, 24, 7, 20, 6, 11, 56, 6, 9, 14, 36, 28, 16, 7, 32, 27, 28, 9, 36, 12, 19, 13, 40, 8, 11, 23, 56, 48, 12, 25, 16, 9, 26, 10, 9, 28, 56, 18, 29, 76, 19, 60, 37, 15, 92, 10, 21, 64, 11, 68, 12, 35, 22, 17, 72, 38

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..73.

Formula

a(n) = A003415(A351048(n)) / A000005(A351048(n)). - Amiram Eldar, Feb 03 2022

Example

a(7) = 4; A351048(7) = 39, so tau(39) = 4 | 16 = 39'. Then a(7) = 39'/tau(39) = 16/4 = 4.

Mathematica

r[1] = 0; r[n_] := Module[{f = FactorInteger[n]}, n * Plus @@ ((Last[#]/First[#]) & /@ f) / Times @@ (1 + Last[#] & /@ f)]; Select[Table[r[n], {n, 1, 500}], IntegerQ] (* Amiram Eldar, Feb 03 2022 *)

Crossrefs

Cf. A000005 (tau), A003415 (arithmetic derivative), A351048.

Sequence in context: A111739 A182214 A339505 * A216161 A332502 A287870

Adjacent sequences: A351160 A351161 A351162 * A351164 A351165 A351166

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 03 2022

Status

approved