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 A351163 Numbers k' / tau(k) such that tau(k) | k'. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers A003415(k) / A000005(k) such that A000005(k) divides A003415(k). LINKS 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

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Last modified March 21 07:27 EDT 2023. Contains 361393 sequences. (Running on oeis4.)