The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A122036 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A122036

Odd abundant numbers (A005231) which are not in A136446, i.e., not sum of some of their proper divisors > 1.
(history; published version)

#45 by N. J. A. Sloane at Sat Feb 12 15:15:56 EST 2022

STATUS

editing

approved

#44 by N. J. A. Sloane at Sat Feb 12 15:15:54 EST 2022

LINKS

<a href="/index/O#oneterm">Index entries for one-term sequences</a>

STATUS

approved

editing

#43 by N. J. A. Sloane at Thu Mar 18 23:38:19 EDT 2021

STATUS

proposed

approved

#42 by M. F. Hasler at Mon Mar 15 12:21:50 EDT 2021

STATUS

editing

proposed

#41 by M. F. Hasler at Mon Mar 15 12:20:44 EDT 2021

KEYWORD

nonn,bref,more,nice,changedhard

STATUS

proposed

editing

Discussion

Mon Mar 15

12:21

M. F. Hasler: + kw "hard" : obviously it's difficult to find a(2) -- and even *any* other term of the sequence!?!

#40 by M. F. Hasler at Mon Mar 15 12:19:27 EDT 2021

STATUS

editing

proposed

#39 by M. F. Hasler at Mon Mar 15 12:19:17 EDT 2021

PROG

(PARI) is_A122036(n)={n>351350 && !is_A005835(n, n=divisors(n)[2..-2]) && n && vecsum(n)>=n[1]*n[#n] && n[1]>2} \\ (Checking for abundant & odd after is_A005835() rather than before, to make it faster when operating on candidates known to satisfy these conditions.) Updated for current PARI syntax by M. F. Hasler, Jul 16 2016, further edits Jan 31 2020

STATUS

proposed

editing

#38 by M. F. Hasler at Mon Mar 15 12:06:53 EDT 2021

STATUS

editing

proposed

#37 by M. F. Hasler at Mon Mar 15 12:06:01 EDT 2021

COMMENTS

a(1) = 351351 = 3^3 * 7 * 11 * 13^2 is the sum of all its 47 proper divisors (including 1) except 7 and 11. -- No other terms congruent to 21 (mod 30) below 10^9. - M. F. Hasler, Jul 16 2016

EXAMPLE

a(1) = 351351 = 3^3 * 7 * 11 * 13^2 is the sum of all its 47 proper divisors (including 1) except 7 and 11, but it is not possible to get the same sum without using the trivial divisor 1: The sum of all proper divisors *larger than 1* yields 351351 + 7 + 11 - 1 = 351351 + 17, and it is not possible to get 17 as sum of a subset of {3, 7, 9, 11, 13, 21, ...}. Thus, 351351 is not in A136446, and therefore in this sequence. - M. F. Hasler, Jul 16 2016, edited Mar 15 2021

EXTENSIONS

Edited by M. F. Hasler, Jul 16 2016, Mar 15 2021

STATUS

approved

editing

Discussion

Mon Mar 15

12:06

M. F. Hasler: Received an email of a reader who did not understand. So I'm moving the example from COMMENTS to EXAMPLE and add some more explanation.

#36 by M. F. Hasler at Fri Jan 31 17:25:00 EST 2020

STATUS

editing

approved