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Revision History for A249746

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A249746

Permutation of natural numbers: a(n) = A126760(A249735(n)) = A249824(A064216(n)).
(history; published version)

#22 by Antti Karttunen at Thu Jul 28 08:04:04 EDT 2016

STATUS

editing

proposed

#21 by Antti Karttunen at Thu Jul 28 08:01:44 EDT 2016

EXAMPLE

a(5) = 9 because of the following. 2*A064216(5) = 2*4 = 8 = 2^3. We replace the prime factor 2 of 8 with the next prime 3 to get 3^3, then replace 3 with 5 to get 5^3 = 125. The smallest prime factor of 125 is 5. 5 125 is the smallest prime factor 9th term of {A084967: 5, 25, 35, 55, 65, 85, 95, 115, 125, ...} and 125 is the 9th term, , thus a(45) = 9.

CROSSREFS

Cf. A003961, A007310, A084967, A126760, A249735, A064216, A249824.

STATUS

approved

editing

Discussion

Thu Jul 28

08:04

Antti Karttunen: Corrected Michael's example.

#20 by Joerg Arndt at Tue Jul 26 02:46:39 EDT 2016

STATUS

reviewed

approved

#19 by Michel Marcus at Tue Jul 26 00:12:49 EDT 2016

STATUS

proposed

reviewed

#18 by Michael De Vlieger at Mon Jul 25 22:02:14 EDT 2016

STATUS

editing

proposed

#17 by Michael De Vlieger at Mon Jul 25 22:01:38 EDT 2016

EXAMPLE

a(5) = 9 because of the following. 2*A064216(5) = 2*4 = 8 = 2^3. We replace the prime factor 2 of 8 with the next prime 3 to get 3^3, then replace 3 with 5 to get 5^3 = 125. The smallest prime factor of 125 is 5. 5 is the smallest prime factor of {5, 25, 35, 55, 65, 85, 95, 115, 125, ...} and 125 is the 9th term, thus a(4) = 9.

MATHEMATICA

t = PositionIndex[FactorInteger[#][[1, 1]] & /@ Range[10^6]]; f[n_] := Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n; Flatten@ Map[Position[Lookup[t, FactorInteger[#][[1, 1]] ], #] &[f@ f[2 #]] &, Table[Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1], {n, 87}]] (* Michael De Vlieger, Jul 25 2016, Version 10 *)

STATUS

approved

editing

Discussion

Mon Jul 25

22:02

Michael De Vlieger: Edited in conjunction with A249824.

#16 by N. J. A. Sloane at Mon Jul 25 21:01:16 EDT 2016

STATUS

proposed

approved

#15 by Antti Karttunen at Mon Jul 25 08:09:46 EDT 2016

STATUS

editing

proposed

#14 by Antti Karttunen at Mon Jul 25 06:39:39 EDT 2016

FORMULA

a(n) = A126760(A249735(n)). - Antti Karttunen, Jul 25 2016

CROSSREFS

Cf. A003961, A007310, A126760, A249735, A064216, A249824.

STATUS

approved

editing

Discussion

Mon Jul 25

06:42

Antti Karttunen: Sequence  A126760 offers a more elegant left inverse for A007310.

06:55

Antti Karttunen: Analogously: A048673(n) = A003602(A003961(n)).

#13 by N. J. A. Sloane at Thu Dec 18 02:02:47 EST 2014

STATUS

proposed

approved