The On-Line Encyclopedia of Integer Sequences (OEIS)

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A331412

Unitary abundant numbers k such that k + 1 is also unitary abundant.
(history; published version)

#21 by Susanna Cuyler at Sat Jan 18 11:07:58 EST 2020

STATUS

proposed

approved

#20 by Amiram Eldar at Sat Jan 18 09:08:42 EST 2020

STATUS

editing

proposed

#19 by Amiram Eldar at Sat Jan 18 09:08:36 EST 2020

LINKS

Giovanni Resta, <a href="/A331412/b331412.txt">Table of n, a(n) for n = 1..1150</a> (terms below 10^13)

STATUS

proposed

editing

#18 by Amiram Eldar at Sat Jan 18 09:02:00 EST 2020

STATUS

editing

proposed

#17 by Amiram Eldar at Sat Jan 18 09:01:54 EST 2020

LINKS

Amiram Eldar, Giovanni Resta, <a href="/A331412/b331412.txt">Table of n, a(n) for n = 1..1150</a>

#16 by Amiram Eldar at Sat Jan 18 09:01:44 EST 2020

LINKS

Amiram Eldar, <a href="/A331412/b331412.txt">Table of n, a(n) for n = 1..1150</a>

STATUS

approved

editing

#15 by Michel Marcus at Sat Jan 18 08:52:50 EST 2020

STATUS

reviewed

approved

#14 by Joerg Arndt at Sat Jan 18 07:31:57 EST 2020

STATUS

proposed

reviewed

#13 by Giovanni Resta at Sat Jan 18 05:43:47 EST 2020

STATUS

editing

proposed

#12 by Amiram Eldar at Sat Jan 18 04:55:31 EST 2020

NAME

allocated for Amiram EldarUnitary abundant numbers k such that k + 1 is also unitary abundant.

DATA

8857357509, 10783550414, 15197873690, 23620285689, 25537083494, 34736070369, 60326914934, 64139567205, 73969772954, 75776483145, 77509981185, 83968675790, 93092467754, 100012014465, 112236593469, 113606741534, 116519300534, 118905484334, 132584489114, 134889106065

OFFSET

1,1

COMMENTS

Apparently most of the terms are squarefree. Up to 10^13 there are 1150 terms, for only 17 terms k either k or k + 1 is nonsquarefree, and there are no terms k such that both k and k + 1 are nonsquarefree. The first nonsquarefree term is a(32) = 285491549265.

EXAMPLE

8857357509 is a term since usigma(8857357509) = 17766604800 > 2 * 8857357509, and usigma(8857357510) = 17851083264 > 2 * 8857357510, where usigma is the sum of unitary divisors function (A034448).

CROSSREFS

Cf. A034448, A034683, A292704.

Analogous sequences: A096399 (regular abundant), A283418 (primitive), A318167 (bi-unitary), A327635 (infinitary), A327942 (nonunitary).

KEYWORD

allocated

nonn

AUTHOR

Amiram Eldar and Giovanni Resta, Jan 18 2020

STATUS

approved

editing