The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A369690

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A369690

a(n) = max(A119288(n), A053669(n)).
(history; published version)

#26 by Michael De Vlieger at Tue Jul 09 08:42:25 EDT 2024

STATUS

reviewed

approved

#25 by Michel Marcus at Tue Jul 09 02:45:33 EDT 2024

STATUS

proposed

reviewed

#24 by Jason Yuen at Tue Jul 09 02:43:38 EDT 2024

STATUS

editing

proposed

#23 by Jason Yuen at Tue Jul 09 02:43:31 EDT 2024

CROSSREFS

Cf. A000079, A002110, A003557, A007947, A024619, A053669, A061345, A096015 (smallest instead of 2nd smallest), A100484, A0119288, A119288, A246547, A361098.

STATUS

approved

editing

#22 by OEIS Server at Sat Mar 09 11:04:24 EST 2024

LINKS

Michael De Vlieger, <a href="/A369690/b369690_1.txt">Table of n, a(n) for n = 1..10000</a>

#21 by N. J. A. Sloane at Sat Mar 09 11:04:24 EST 2024

STATUS

editing

approved

Discussion

Sat Mar 09

11:04

OEIS Server: Installed first b-file as b369690.txt.

#20 by Michael De Vlieger at Fri Mar 08 17:26:17 EST 2024

FORMULA

Let P(n) = A002110(n) and let rad(n) = A007947(n).

a(n) = prime(j) for j > 2 and both { k = m*P(j-1) : rad(m) | P(j-1) } and for d | P(j) such that omega(d) = 2, prime(j-1) | d, and d < P(j), k in { k = m*d : rad(m) | d }.

Discussion

Fri Mar 08

17:27

Michael De Vlieger: I'll append the write up as an a-file, since the formula was pretty complicated. Will finalize it and send offline before posting here.

#19 by Peter Munn at Fri Feb 23 09:00:04 EST 2024

COMMENTS

Equivalently, a(n) is the maximum of a set of candidates, where a number is a candidate if it largest p such that p is the 2nd smallest prime dividing n or the smallest prime not dividing n.

CROSSREFS

Cf. A000079, A002110, A003557, A007947, A024619, A053669, A061345, A096015, (smallest instead of 2nd smallest), A100484, A0119288, A246547, A361098.

Discussion

Fri Feb 23

09:03

Peter Munn: Will formulate a comment about its use with A003557 to divide the integers into 2 sets with positive asymptotic density.

09:17

Peter Munn: Mike, I struggle to figure where to put the semantic brackets in the second formula. Is it possible for us to break it into two or split more text out with another "Let symbol = ..."?

20:22

Michael De Vlieger: Looking into it!

Fri Mar 01

16:52

Peter Munn: Meanwhile, I've been making progress in understanding the related sequences...

#18 by Peter Munn at Wed Feb 21 01:47:49 EST 2024

CROSSREFS

Cf. A000079, A002110, A003557, A007947, A024619, A053669, A061345, A096015, A100484, A0119288, A246547, A361098.

#17 by Peter Munn at Wed Feb 21 01:21:49 EST 2024

COMMENTS

a(n) is the maximum of a set of candidates, where a number is a candidate if it is the 2nd smallest prime dividing n or the smallest prime not dividing n.