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Minimal numbers (with respect to division) with no coprime divisor shift.
3

%I #21 Oct 14 2023 07:55:52

%S 2,15,33,51,69,87,123,141,159,177,213,249,267,303,321,339,393,411,447,

%T 501,519,537,573,591,665,681,699,717,753,771,789,807,819,843,879,933,

%U 951,1015,1041,1059,1077,1149,1167,1203,1235,1257,1293,1329,1347,1383

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

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

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

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

%D a(1) = 2 for GCD(2 + 0, 2) > 1 and GCD(1 + 1, 2) > 1.

%D 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.

%H M. Farrokhi D. G., <a href="/A366330/b366330.txt">Table of n, a(n) for n = 1..10000</a>

%Y Cf. A044135, A044516, A366219, A366251.

%K nonn

%O 1,1

%A _M. Farrokhi D. G._, Oct 07 2023