The On-Line Encyclopedia of Integer Sequences (OEIS)

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A329883

Nonunitary highly abundant numbers: numbers m such that nusigma(m) > nusigma(k) for all k < m, where s(n) is the sum of nonunitary divisors of n (A048146).
(history; published version)

#9 by OEIS Server at Fri Jan 12 01:28:22 EST 2024

LINKS

Amiram Eldar, <a href="/A329883/b329883_1.txt">Table of n, a(n) for n = 1..500</a>

#8 by Michel Marcus at Fri Jan 12 01:28:22 EST 2024

STATUS

reviewed

approved

Discussion

Fri Jan 12

01:28

OEIS Server: Installed first b-file as b329883.txt.

#7 by Joerg Arndt at Fri Jan 12 00:27:35 EST 2024

STATUS

proposed

reviewed

#6 by Amiram Eldar at Fri Jan 12 00:21:29 EST 2024

STATUS

editing

proposed

#5 by Amiram Eldar at Fri Jan 12 00:14:19 EST 2024

LINKS

Amiram Eldar, <a href="/A329883/b329883_1.txt">Table of n, a(n) for n = 1..500</a>

STATUS

approved

editing

#4 by N. J. A. Sloane at Sat Nov 23 23:14:10 EST 2019

STATUS

proposed

approved

#3 by Amiram Eldar at Sat Nov 23 16:20:36 EST 2019

STATUS

editing

proposed

#2 by Amiram Eldar at Sat Nov 23 16:00:38 EST 2019

NAME

allocated Nonunitary highly abundant numbers: numbers m such that nusigma(m) > nusigma(k) for Amiram Eldarall k < m, where s(n) is the sum of nonunitary divisors of n (A048146).

DATA

1, 4, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96, 108, 120, 144, 180, 192, 216, 288, 360, 432, 504, 576, 648, 720, 864, 1008, 1080, 1296, 1440, 1728, 1800, 2016, 2160, 2520, 2880, 3024, 3240, 3456, 3528, 3600, 4320, 5040, 5400, 5760, 6048, 6480, 7056, 7200, 8640

OFFSET

1,2

COMMENTS

The corresponding record values are 0, 2, 6, 8, 14, 24, 30, 41, 56, 62, 105, 120, 140, 144, 233, 246, 248, 348, 489, 630, 764, 840, ...

MATHEMATICA

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); nusigma[n_] := DivisorSigma[1, n] - usigma[n]; num = -1; s = {}; Do[nu = nusigma[n]; If[nu > num, num = nu; AppendTo[s, n]], {n, 1, 10^4}]; s

CROSSREFS

The nonunitary version of A002093.

Cf. A048146, A064597, A309141, A329882.

KEYWORD

allocated

nonn

AUTHOR

Amiram Eldar, Nov 23 2019

STATUS

approved

editing

#1 by Amiram Eldar at Sat Nov 23 16:00:38 EST 2019

NAME

allocated for Amiram Eldar

KEYWORD

allocated

STATUS

approved