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

1,1

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.

Links

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

Formula

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A321497 A335084 A133688 * A115414 A358412 A112430

Adjacent sequences: A306494 A306495 A306496 * A306498 A306499 A306500

Keyword

nonn

Author

Sergio Pimentel, Feb 19 2019

Extensions

More terms from Amiram Eldar, Jul 16 2019

Status

approved