A258912 Numbers k such that A000203(x) = k has more than one solution and they all share the same largest prime factor.

1178, 1364, 1408, 1656, 1767, 1836, 1922, 1984, 2108, 2196, 2328, 2368, 3162, 3336, 3410, 3996, 4096, 4123, 4144, 4278, 4898, 5064, 5076, 5084, 5248, 5456, 5488, 5673, 6014, 6208, 6504, 6784, 6816, 7416, 7998, 8618, 8896, 9088, 9184, 9517, 10048, 10292, 10864

Offset: 1

Author

Michel Marcus, Jun 14 2015

Keywords

• nonn

Comments

By definition this is a subsequence of A159886.

Pollack shows that the density of such integers relative to A002191 is 1.

Examples

			The pre-image of 1178 is [592, 925], and both have greatest prime factor 37, so 1178 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Paul Pollack, Remarks on fibers of the sum-of-divisors function, Analytic number theory (volume in honor of H. Maier), M. Rassias and C. Pomerance, eds., Springer, 2015, alternative link.

Crossrefs

Cf. A000203 (sum of divisors), A002191 (possible values of sum of divisors), A159886 (sigma(x)=n has more than one solution).

Programs

PARI

isok(n) = {my(v = select(x->sigma(x)==n, vector(n, i, i))); if (#v < 2, return (0)); vgpf = vector(#v, k, fvk = factor(v[k]); fvk[#fvk~,1]); vecmin(vgpf) == vecmax(vgpf);}