The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A219108 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A219108

a(n) = k is the smallest number such that k^3 + 1 has exactly n distinct prime factors.
(history; published version)

#45 by Michel Marcus at Mon Sep 18 06:17:54 EDT 2023

STATUS

reviewed

approved

#44 by Joerg Arndt at Mon Sep 18 02:15:54 EDT 2023

STATUS

proposed

reviewed

#43 by Andrew Howroyd at Tue Sep 12 16:12:43 EDT 2023

STATUS

editing

proposed

#42 by Andrew Howroyd at Tue Sep 12 16:12:38 EDT 2023

PROG

(PARI) a(n)=for(k=0, oo, if(omega(k^3+1) == n, return(k))) \\ Andrew Howroyd, Sep 12 2023

STATUS

proposed

editing

#41 by Pontus von Brömssen at Tue Sep 12 14:51:07 EDT 2023

STATUS

editing

proposed

#40 by Pontus von Brömssen at Tue Sep 12 14:40:04 EDT 2023

EXTENSIONS

Name clarified and incorrect programs program removed by Pontus von Brömssen, Sep 12 2023

Discussion

Tue Sep 12

14:46

Pontus von Brömssen: Following up on the discussion in A180278, I deleted the first Mma program because it looks for *at least* n prime factors. In this case it's clear from the formula that *exactly* n factors is the intended meaning. The second Mma seems correct (except that it misses the first term), but produces terms of the form (n,a(n)), which are not ordered by n but by a(n) (if the sequence is not increasing).

#39 by Pontus von Brömssen at Tue Sep 12 14:39:52 EDT 2023

NAME

a(n) = k is the smallest number such that k^3 + 1 has exactly n distinct prime factors.

MATHEMATICA

Join[{0}, Table[k = 1; While[Length[FactorInteger[k^3 + 1]] < n, k++]; k, {n, 10}]] (* T. D. Noe, Nov 12 2012 *)

EXTENSIONS

Name clarified and incorrect programs removed by Pontus von Brömssen, Sep 12 2023

STATUS

approved

editing

#38 by Michael De Vlieger at Tue Sep 06 10:30:59 EDT 2022

STATUS

reviewed

approved

#37 by Joerg Arndt at Tue Sep 06 06:03:32 EDT 2022

STATUS

proposed

reviewed

#36 by Michel Marcus at Tue Sep 06 03:25:14 EDT 2022

STATUS

editing

proposed