The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A096536 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A096536

Numbers k such that k, k+1, k+2 are all abundant.
(history; published version)

#36 by Joerg Arndt at Sat Nov 19 04:32:11 EST 2022

STATUS

reviewed

approved

#35 by Amiram Eldar at Sat Nov 19 04:00:50 EST 2022

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proposed

reviewed

#34 by Michel Marcus at Sat Nov 19 02:31:03 EST 2022

STATUS

editing

proposed

#33 by Michel Marcus at Sat Nov 19 02:30:57 EST 2022

PROG

(PARI) isab(x) = sigma(x) > 2*x; \\ A005101

isok(k) = isab(k) && isab(k+1) && isab(k+2); \\ Michel Marcus, Nov 19 2022

STATUS

approved

editing

#32 by OEIS Server at Sun Oct 02 10:32:33 EDT 2022

LINKS

Amiram Eldar, <a href="/A096536/b096536_1.txt">Table of n, a(n) for n = 1..22583</a> (terms below 10^12; terms 1..1000 from Donovan Johnson)

#31 by Michael De Vlieger at Sun Oct 02 10:32:33 EDT 2022

STATUS

reviewed

approved

Discussion

Sun Oct 02

10:32

OEIS Server: Installed new b-file as b096536.txt.  Old b-file is now b096536_1.txt.

#30 by Joerg Arndt at Sun Oct 02 02:28:39 EDT 2022

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proposed

reviewed

#29 by Amiram Eldar at Sun Oct 02 02:23:59 EDT 2022

STATUS

editing

proposed

#28 by Amiram Eldar at Sun Oct 02 02:08:04 EDT 2022

COMMENTS

From Amiram Eldar, Oct 02 2022: (Start)

The least term that is == 1 (mod 3) is a(1292) = 55959128224, and the least term that is divisible by 3 is a(1590) = 68972878974.

The numbers of terms not exceeding 10^k, for k = 9, 10, ..., are 9, 226, 2298, 22583, ... . Apparently, the asymptotic density of this sequence exists and equals 2.2...*10^(-8). (End)

#27 by Amiram Eldar at Sun Oct 02 02:07:16 EDT 2022

EXAMPLE

For 171078830 = 2*5*13*23*29*1973, sigma(n)/n = 2.09355, for 171078831 = 3^3*7*11*19*61*71, sigma(n)/n = 2.00396 and for 171078832 = 2^4*31*344917, sigma(n)/n = 2.00000579.