The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A348604 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A348604

Nonexponential abundant numbers: numbers k such that A160135(k) > k.
(history; published version)

#11 by Peter Luschny at Tue Oct 26 04:27:39 EDT 2021

STATUS

reviewed

approved

#10 by Michel Marcus at Tue Oct 26 03:02:49 EDT 2021

STATUS

proposed

reviewed

#9 by Amiram Eldar at Tue Oct 26 02:14:18 EDT 2021

STATUS

editing

proposed

#8 by Amiram Eldar at Tue Oct 26 02:13:36 EDT 2021

COMMENTS

The number numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 13, 148, 1595, 15688, 158068, 1578957, 15762209, 157745113, 1577808429, ... Apparently this sequence has an asymptotic density 0.157...

#7 by Amiram Eldar at Tue Oct 26 01:26:10 EDT 2021

COMMENTS

The number of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 13, 148, 1595, 15688, 158068, 1578957, 15762209, 157745113, 1577808429, ... Apparently this sequence has an asymptotic density 0.157...

#6 by Amiram Eldar at Tue Oct 26 01:25:27 EDT 2021

LINKS

Amiram Eldar, <a href="/A348604/b348604.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#5 by N. J. A. Sloane at Mon Oct 25 11:11:55 EDT 2021

STATUS

proposed

approved

#4 by Amiram Eldar at Mon Oct 25 02:14:34 EDT 2021

STATUS

editing

proposed

#3 by Amiram Eldar at Mon Oct 25 01:58:35 EDT 2021

CROSSREFS

Similar sequences: A034683, A064597, A129575, A129656, A292982, A348274.

#2 by Amiram Eldar at Mon Oct 25 01:57:45 EDT 2021

NAME

allocated for Amiram EldarNonexponential abundant numbers: numbers k such that A160135(k) > k.

DATA

24, 30, 42, 48, 54, 60, 66, 70, 72, 78, 84, 90, 96, 102, 114, 120, 126, 132, 138, 150, 156, 160, 162, 168, 174, 180, 186, 192, 198, 210, 216, 222, 224, 240, 246, 258, 264, 270, 280, 282, 288, 294, 300, 312, 318, 320, 330, 336, 352, 354, 360, 366, 378, 384, 390

OFFSET

1,1

COMMENTS

The smallest odd term is a(1357) = 8505.

EXAMPLE

24 is a term since A160135(24) = 30 > 24.

MATHEMATICA

esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; q[n_] := DivisorSigma[1, n] - esigma[n] > n; Select[Range[400], q]

CROSSREFS

Cf. A160135, A348601.

Subsequence of A005101.

Similar sequences: A034683, A064597, A129575, A129656, A292982.

KEYWORD

allocated

nonn

AUTHOR

Amiram Eldar, Oct 25 2021

STATUS

approved

editing