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Abundant numbers that differ from the next abundant number by 5.
3

%I #36 Apr 11 2021 16:14:28

%S 5391411025,26957055120,28816162375,33426748350,34393484125,

%T 37739877175,40342627320,48150877770,50866790970,53356378075,

%U 59305521270,60711976320,61164628525,63395557225,64899009175,67275433225,70088343325,74922022170,75665665075,76781129425

%N Abundant numbers that differ from the next abundant number by 5.

%C Since all multiples of 6 are abundant, numbers in this sequence have to be abundant numbers of the form 6n or 6n + 1. Most common difference between abundant numbers is 6, followed by 2, 4, 3, 1. 5 is the least common.

%H David A. Corneth, <a href="/A306497/b306497.txt">Table of n, a(n) for n = 1..10000</a>

%F Either a(n) or a(n)+5 are in A115414. - _Amiram Eldar_, Jul 16 2019

%e a(1) = 5391411025 is in the sequence since it is abundant and the next abundant number is 5391411030 which is a(1)+5 and all the numbers in between are deficient.

%o (PARI) isok(n) = for(k=1, 4, if(sigma(n+k) > 2*(n+k), return(0))); (sigma(n) > 2*n) && (sigma(n+5) > 2*(n+5)); \\ _Daniel Suteu_, Jul 24 2019

%Y Cf. A005101, A096399, A231086, A228382, A316098, A316099, A115414, A125115.

%K nonn

%O 1,1

%A _Sergio Pimentel_, Feb 19 2019

%E More terms from _Amiram Eldar_, Jul 16 2019