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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Complement of the union of A003594 and A160545. Analogous to A081062 and A105115 regarding terms 1 and 2 of A120944, respectively. This sequence applies to A120944(5) = 21. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 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: select(filter, [\$1..200]); # Robert Israel, Aug 28 2019 MATHEMATICA With[{nn = 161, k = 21}, Select[Range@ nn, And[1 < GCD[#, k] < #, PowerMod[k, Floor@ Log2@ nn, #] != 0] &]] CROSSREFS Cf. A003594, A081062, A105115, A120944, A160545. Sequence in context: A366532 A325700 A360551 * A246048 A348251 A290648 Adjacent sequences: A306996 A306997 A306998 * A307000 A307001 A307002 KEYWORD nonn,easy AUTHOR Michael De Vlieger, Aug 22 2019 STATUS approved

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Last modified August 8 15:25 EDT 2024. Contains 375022 sequences. (Running on oeis4.)