A306497 Abundant numbers that differ from the next abundant number by 5.

5391411025, 26957055120, 28816162375, 33426748350, 34393484125, 37739877175, 40342627320, 48150877770, 50866790970, 53356378075, 59305521270, 60711976320, 61164628525, 63395557225, 64899009175, 67275433225, 70088343325, 74922022170, 75665665075, 76781129425

Offset: 1

Author

Sergio Pimentel, Feb 19 2019

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

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

Formula

Either a(n) or a(n)+5 are in A115414. - Amiram Eldar, Jul 16 2019

Extensions

More terms from Amiram Eldar, Jul 16 2019