The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A329900 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A329900

Primorial deflation of n: starting from x = n, repeatedly divide x by the largest primorial A002110(k) that divides it, until x is an odd number. Then a(n) = Product prime(k_i), for primorial indices k_1 >= k_2 >= ..., encountered in the process.
(history; published version)

#54 by Alois P. Heinz at Sun Jan 12 12:47:47 EST 2020

STATUS

reviewed

approved

#53 by Joerg Arndt at Sun Jan 12 10:18:57 EST 2020

STATUS

proposed

reviewed

#52 by Michael De Vlieger at Sat Jan 11 22:29:07 EST 2020

STATUS

editing

proposed

#51 by Michael De Vlieger at Sat Jan 11 22:29:03 EST 2020

MATHEMATICA

Array[Times @@ Prime@(TakeWhile[Reap[FixedPointList[Block[{k = 1}, While[Mod[#, Prime@ k] == 0, k++]; Sow[k - 1]; #/Product[Prime@ i, {i, k - 1}]] &, #]][[-1, 1]], # > 0 &]) &, 105] (* Michael De Vlieger, Jan 11 2020 *)

STATUS

approved

editing

#50 by N. J. A. Sloane at Sun Dec 29 10:35:39 EST 2019

STATUS

proposed

approved

#49 by Daniel Suteu at Sun Dec 29 07:20:23 EST 2019

STATUS

editing

proposed

Discussion

Sun Dec 29

07:57

Daniel Suteu: All good. Ready for review.

#48 by Antti Karttunen at Sun Dec 29 06:07:00 EST 2019

CROSSREFS

A left inverse of A108951. Coincides with A319626 on A025487.

Cf. A002110, A002182, A025487, A111701, A181815, A181817, A181819, A181821, A276084, A304886, A319626, A319627, A328478, A328479, A329889, A329902, A330685, A330686, A330689.

#47 by Antti Karttunen at Sun Dec 29 05:51:33 EST 2019

COMMENTS

According to Daniel Suteu, also the ratio (A319626(n) / A319627(n)) can be viewed as a "primorial deflation". Note that on any That definition coincides with this one when restricted to terms of A025487, as for all k in A025487, A319626(k) = a(k), and A319627(k) = 1. - Antti Karttunen, Dec 29 2019

Discussion

Sun Dec 29

05:55

Antti Karttunen: Asking for Daniel's for any further comments on this...

#46 by Antti Karttunen at Sun Dec 29 05:49:10 EST 2019

CROSSREFS

Cf. A002110, A002182, A025487, A111701, A181815, A181817, A181819, A181821, A276084, A304886, A319626, A319627, A328478, A328479, A329889, A329902, A330685, A330686, A330689.

#45 by Antti Karttunen at Sun Dec 29 05:47:59 EST 2019

COMMENTS

According to Daniel Suteu, also the ratio (A319626(n) / A319627(n)) can be viewed as a "primorial deflation". Note that on any k in A025487, A319626(k) = a(k), and A319627(k) = 1. - Antti Karttunen, Dec 29 2019

STATUS

proposed

editing