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

1,1

Comments

By definition this is a subsequence of A159886.

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

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.

Example

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

Prog

(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); }

Crossrefs

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

Sequence in context: A223340 A270147 A270114 * A237094 A321867 A210847

Adjacent sequences: A258909 A258910 A258911 * A258913 A258914 A258915

Keyword

nonn

Author

Michel Marcus, Jun 14 2015

Status

approved