A366330 Minimal numbers (with respect to division) with no coprime divisor shift.

2, 15, 33, 51, 69, 87, 123, 141, 159, 177, 213, 249, 267, 303, 321, 339, 393, 411, 447, 501, 519, 537, 573, 591, 665, 681, 699, 717, 753, 771, 789, 807, 819, 843, 879, 933, 951, 1015, 1041, 1059, 1077, 1149, 1167, 1203, 1235, 1257, 1293, 1329, 1347, 1383

Offset: 1

Author

M. Farrokhi D. G., Oct 07 2023

Keywords

• nonn

Comments

A number k has a coprime divisor shift s if GCD(d + s, n) = 1 for all divisors d of k.

A number k has a coprime divisor shift iff it is not divisible by any number in the sequence.

If k has no coprime divisor shift, then so is any multiple of k.

References

• a(1) = 2 for GCD(2 + 0, 2) > 1 and GCD(1 + 1, 2) > 1.
• a(2) = 15 for GCD(3 + 0, 15) > 1, GCD(5 + 1, 15) > 1, GCD(1 + 2, 15) > 1, and any odd number between 2 and 15 has a coprime divisor shift.

Links

• M. Farrokhi D. G., Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A044135, A044516, A366219, A366251.