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

1,1

Links

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

Example

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.

Prog

(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

Crossrefs

Intersection of A070003 and A336353.

Cf. A000203, A006530, A319988, A336352.

Sequence in context: A045269 A373590 A043395 * A269346 A202852 A117689

Adjacent sequences: A336351 A336352 A336353 * A336355 A336356 A336357

Keyword

nonn

Author

Antti Karttunen, Jul 19 2020

Status

approved