[seqfan] a(n) | n

Frank Adams-Watters franktaw at netscape.net
Thu Jan 25 20:36:56 CET 2018

I've been looking recently at sequences where a(n) divides n for every n > 0. 

These come naturally in pairs, whose element-wise product is n.

Here's a list, which is by no means complete:

A000012 * A000027
A000034 * A026741
A000265 * A006519
A003557 * A007947
A006530 * A052126
A007913 * A008833
A020639 * A032742
A028233 * A028234
A033676 * A033677
A034699 * A284600
A060789 * A089128
A065330 * A065331
A060775 * A140271
A122377 * A298734

(A298734 I have just submitted.)

It seems to me that this should be documented somewhere in the OEIS, but I'm not sure where. (Maybe in the index file somewhere?)

Preserving this property is for me one good reason to have a(1) = 1 in sequences like A020439 (least prime factor) where a(1) is otherwise undefined.

Franklin T. Adams-Watters

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