The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A091011 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A091011

Numbers having at least one divisor, d, such that for some x, d-x and d+x are also divisors.
(history; published version)

#8 by Wesley Ivan Hurt at Mon Feb 01 18:18:14 EST 2021

STATUS

editing

approved

#7 by Wesley Ivan Hurt at Mon Feb 01 18:18:11 EST 2021

FORMULA

Characteristic function: sign( Sum_{d1|n, d2|n, 2|(d1+d2), (d1+d2)|(2*n), d1<d2} 1 ). - Wesley Ivan Hurt, Aug 23 2020

STATUS

approved

editing

#6 by N. J. A. Sloane at Mon Aug 24 22:46:06 EDT 2020

STATUS

proposed

approved

#5 by Wesley Ivan Hurt at Mon Aug 24 01:21:08 EDT 2020

STATUS

editing

proposed

#4 by Wesley Ivan Hurt at Sun Aug 23 23:43:09 EDT 2020

NAME

Numbers having at least one divisor , d , such that for some x also , d-x and d+x are also divisors.

COMMENTS

Numbers k with at least one pair of divisors, (d1,d2), with d1 < d2, whose (integer) average divides k. - Wesley Ivan Hurt, Aug 23 2020

FORMULA

Characteristic function: sign( Sum_{d1|n, d2|n, 2|(d1+d2), (d1+d2)|(2*n), d1<d2} 1 ). - Wesley Ivan Hurt, Aug 23 2020

MATHEMATICA

Table[If[Sum[Sum[(1 - Ceiling[(i + k)/2] + Floor[(i + k)/2]) (1 - Ceiling[2 n/(i + k)] + Floor[2 n/(i + k)]) (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k - 1}], {k, n}] > 0, n, {}], {n, 200}] // Flatten (* Wesley Ivan Hurt, Aug 23 2020 *)

CROSSREFS

Cf. A091009, A091010, A337331.

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 18:50:43 EDT 2012

AUTHOR

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Dec 13 2003

Discussion

Fri Mar 30

18:50

OEIS Server: https://oeis.org/edit/global/246

#2 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystemsgmail.com), Dec 13 2003

#1 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

NAME

Numbers having at least one divisor d such that for some x also d-x and d+x are divisors.

DATA

6, 12, 15, 18, 24, 28, 30, 36, 40, 42, 45, 48, 54, 56, 60, 66, 72, 75, 78, 80, 84, 90, 91, 96, 102, 105, 108, 112, 114, 120, 126, 132, 135, 138, 140, 144, 150, 153, 156, 160, 162, 165, 168, 174, 180, 182, 186, 190, 192, 195, 196, 198, 200, 204, 210, 216, 220

OFFSET

1,1

COMMENTS

A091009(a(n)) > 0; complement of A091010.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Dec 13 2003

STATUS

approved