A336354 Numbers k such that p^2 divides k, where p = A006530(k), the largest prime factor of k, and sigma(k) does not have any prime factor larger than p.

343, 686, 1029, 1372, 1715, 2058, 2744, 3430, 4116, 4489, 5145, 6241, 6860, 8232, 8978, 9261, 10290, 10976, 12482, 13467, 13720, 17956, 18522, 18723, 18769, 20580, 22201, 22445, 24964, 26569, 26934, 31205, 31423, 32761, 32928, 35912, 36481, 37044, 37446, 37538, 40401

Offset: 1

Author

Antti Karttunen, Jul 19 2020

Keywords

• nonn

Examples

			343 = 7^3 is present, as A000203(343) = 400 = 2^4 * 5^2, with none of the prime factors > 7.
1715 = 5 * 7^3 is present, as sigma(1715) = 2400 = 2^5 * 3 * 5^2.
		

Links

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

Crossrefs

Intersection of A070003 and A336353.

Cf. A000203, A006530, A319988, A336352.

Programs

PARI

isA336354(n) = ((0==A336352(n))&&(1==A319988(n)));

PARI

is(n) = {if(n == 1, return(0));
	my(f = factor(n), s, fs);
	if(f[#f~, 2] < 2, return(0));
	s = sigma(f);
	fs = factor(s, f[#f~, 1]);
	fs[#fs~, 1] <= f[#f~, 1]
} \\ David A. Corneth, Jun 27 2024