The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A332696 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A332696

Sum of the proper divisors of n such that d, n/d and n-d are all squarefree.
(history; published version)

#52 by Peter Luschny at Tue Apr 28 13:01:10 EDT 2020

STATUS

reviewed

approved

#51 by Joerg Arndt at Tue Apr 28 11:51:55 EDT 2020

STATUS

proposed

reviewed

#50 by Joerg Arndt at Tue Apr 28 11:51:51 EDT 2020

STATUS

editing

proposed

#49 by Joerg Arndt at Tue Apr 28 11:51:47 EDT 2020

COMMENTS

a(p^k) = p^(k-1) * mu(p-1)^2 for k = 1 or 2, and 0 for k > 2.

If p is an odd prime, a(2*p) = p + mu(2*p-1)^2. - Robert Israel, Apr 28 2020

FORMULA

a(p^k) = p^(k-1) * mu(p-1)^2 for k = 1 or 2, and 0 for k > 2.

If p is an odd prime, a(2*p) = p + mu(2*p-1)^2. - Robert Israel, Apr 28 2020

STATUS

proposed

editing

#48 by Robert Israel at Tue Apr 28 11:21:28 EDT 2020

STATUS

editing

proposed

Discussion

Tue Apr 28

11:26

Michel Marcus: the 2 comments are formulas ?

#47 by Robert Israel at Tue Apr 28 11:21:08 EDT 2020

COMMENTS

If p is an odd prime, a(2*p) = p + mu(2*p-1)^2. - Robert Israel, Apr 28 2020

#46 by Robert Israel at Tue Apr 28 11:13:46 EDT 2020

KEYWORD

nonn,easy,new,look

#45 by Robert Israel at Tue Apr 28 11:03:37 EDT 2020

LINKS

Robert Israel, <a href="/A332696/b332696.txt">Table of n, a(n) for n = 1..10000</a>

MAPLE

f:= proc(n) uses numtheory;

convert(select(t-> issqrfree(t) and issqrfree(n/t) and issqrfree(n-t), divisors(n) minus {n}), `+`)

end proc:

map(f, [$1..100]); # Robert Israel, Apr 28 2020

STATUS

approved

editing

#44 by Wesley Ivan Hurt at Mon Apr 27 00:23:36 EDT 2020

STATUS

proposed

approved

#43 by Wesley Ivan Hurt at Sun Apr 26 15:16:41 EDT 2020

STATUS

editing

proposed