The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A284785 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A284785

a(n) = rad(A280864(n)).
(history; published version)

#23 by N. J. A. Sloane at Tue Apr 11 08:17:13 EDT 2017

STATUS

editing

approved

#22 by N. J. A. Sloane at Tue Apr 11 08:17:10 EDT 2017

COMMENTS

Theorem: a(n) = b(n-1)*b(n) where b = A280738. - N. J. A. Sloane, Apr 11 2017

CROSSREFS

Cf. A280864, A284311, A284457, A007947, A280738.

STATUS

approved

editing

#21 by N. J. A. Sloane at Tue Apr 11 08:07:19 EDT 2017

STATUS

editing

approved

#20 by N. J. A. Sloane at Tue Apr 11 08:07:15 EDT 2017

COMMENTS

Even terms appear consecutively in pairs, each pair followed by a series of consecutive one or more odd terms.

CROSSREFS

Cf. A280864, A284311, A284457, A007947.

Cf. A007947.

STATUS

proposed

editing

#19 by Bob Selcoe at Tue Apr 11 00:37:02 EDT 2017

STATUS

editing

proposed

#18 by Bob Selcoe at Tue Apr 11 00:36:59 EDT 2017

COMMENTS

By definition, all terms are squarefree (see A007947); repeated terms here are found in a single column the squarefree kernels of A284311A280864(n).

STATUS

proposed

editing

#17 by Bob Selcoe at Mon Apr 10 16:56:08 EDT 2017

STATUS

editing

proposed

#16 by Bob Selcoe at Mon Apr 10 16:55:25 EDT 2017

EXAMPLE

a(61) = 30 because A280864(61) = 60 = 2^2*3*5 , and therefore is rad(60) = 30).

STATUS

proposed

editing

Discussion

Mon Apr 10

16:56

Bob Selcoe: Rather needed to revise example; should be ok now.

#15 by Bob Selcoe at Mon Apr 10 16:47:29 EDT 2017

STATUS

editing

proposed

Discussion

Mon Apr 10

16:49

Bob Selcoe: Wait please- need to revise name...

#14 by Bob Selcoe at Mon Apr 10 16:44:39 EDT 2017

NAME

A280864(n) by membership in "radical class" (see Comments for definition).

a(n) = rad(A280864(n)).

COMMENTS

Define "radical class" C_R to be the set of numbers which have the same radical (or the same largest squarefree divisor - i.e., the same product of their prime factors,), where R is the radical (or squarefree kernel). These are the columns in A284311. So for example, C_10 is the set of numbers with radical 10, i.e., prime factors {2,5}: {10, 20, 40, 50 80, 100, 160, ...}. Powers of prime P are simply C_P.

By definition, all terms are squarefree (see A007947); repeated terms are found in a single column of A284311.

EXAMPLE

a(61) = 30 because A280864(61) = 60 = 2^2*3*5 and therefore is in C_rad(30).

CROSSREFS

Cf. A007947.

Discussion

Mon Apr 10

16:47

Bob Selcoe: @Neil - if I understand the proper terminology, I think the revisions are OK, and no need to introduce the "radical class" idea here.  I hope it's therefore OK to change the name.