A358413 - OEIS

%I #18 Nov 15 2022 17:51:41

%S 180,1018976683725,

%T 5164037398437051798923642083026622326955987448536772329145127064375

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

%C 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.

%H Jianing Song, <a href="/A358413/b358413.txt">Table of n, a(n) for n = 0..4</a>

%H Mercurial, the Spectre, <a href="http://hi.gher.space/forum/viewtopic.php?f=11&amp;t=2248&amp;sid=cbf9e6743a4ccdcd6cbcadcdf56946db">Abundant numbers coprime to n</a>, Hi.gher. Space.

%e a(1) = A119240(3) = 1018976683725 is the smallest 3-abundant odd number.

%e a(2) = A358412(3) = 5164037398437051798923642083026622326955987448536772329145127064375 is the smallest 3-abundant number that is coprime to 2 and 3.

%Y Cf. A068403 (3-abundant numbers).

%Y 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).

%Y 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).

%K nonn,bref,hard

%O 0,1

%A _Jianing Song_, Nov 14 2022