

A306999


Numbers m such that 1 < gcd(m, 21) < m and m does not divide 21^e for e >= 0.


4



6, 12, 14, 15, 18, 24, 28, 30, 33, 35, 36, 39, 42, 45, 48, 51, 54, 56, 57, 60, 66, 69, 70, 72, 75, 77, 78, 84, 87, 90, 91, 93, 96, 98, 99, 102, 105, 108, 111, 112, 114, 117, 119, 120, 123, 126, 129, 132, 133, 135, 138, 140, 141, 144, 150, 153, 154, 156, 159, 161
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OFFSET

1,1


COMMENTS



LINKS



EXAMPLE

6 is in the sequence since gcd(6, 21) = 3 and 6 does not divide 21^e with integer e >= 0.
5 is not in the sequence since it is coprime to 21.
3 is not in the sequence since 3  21.
9 is not in the sequence since 9  21^2.


MAPLE

filter:= proc(n) local g;
g:= igcd(n, 21);
if g = 1 or g = n then return false fi;
3^padic:ordp(n, 3)*7^padic:ordp(n, 7) < n
end proc:


MATHEMATICA

With[{nn = 161, k = 21}, Select[Range@ nn, And[1 < GCD[#, k] < #, PowerMod[k, Floor@ Log2@ nn, #] != 0] &]]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



