A358413 Smallest 3-abundant number (sigma(x) > 3x) which is not divisible by any of the first n primes.

180, 1018976683725, 5164037398437051798923642083026622326955987448536772329145127064375

Offset: 0

Author

Jianing Song, Nov 14 2022

Keywords

• nonn
• bref
• hard

Comments

Data copied from the Hi.gher. Space link where Mercurial, the Spectre calculated the terms. We have a(0) = 2^2*3^2*5, a(1) = 3^3*5^2*7^2*11*13*17*19*23*29, and a(2) = 5^4*7^3*11^2*13^2*17*...*157 ~ 5.16404*10^66. a(3) = 7^3*11^3*13^2*17^2*19^2*23^2*29^2*31*...*569 ~ 2.54562*10^239 and a(4) = 11^3*13^3*17^2*...*47^2*53*...*1597 ~ 3.99515*10^688 are too large to display.

Examples

			a(1) = A119240(3) = 1018976683725 is the smallest 3-abundant odd number.
a(2) = A358412(3) = 5164037398437051798923642083026622326955987448536772329145127064375 is the smallest 3-abundant number that is coprime to 2 and 3.
		

Links

• Jianing Song, Table of n, a(n) for n = 0..4
• Mercurial, the Spectre, Abundant numbers coprime to n, Hi.gher. Space.

Crossrefs

Cf. A068403 (3-abundant numbers).

Smallest k-abundant number which is not divisible by any of the first n primes: A047802 (k=2), this sequence (k=3), A358414 (k=4).

Least p-rough number k such that sigma(k)/k >= n: A023199 (p=2), A119240 (p=3), A358412 (p=5), A358418 (p=7), A358419 (p=11).