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A366330
Minimal numbers (with respect to division) with no coprime divisor shift.
3
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
1,1
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
CROSSREFS
KEYWORD
nonn
AUTHOR
M. Farrokhi D. G., Oct 07 2023
STATUS
approved