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A244416 6-adic value of 1/n for n >= 1.

%I A244416 #13 Aug 19 2024 12:16:08
%S A244416 1,6,6,36,1,6,1,216,36,6,1,36,1,6,6,1296,1,36,1,36,6,6,1,216,1,6,216,
%T A244416 36,1,6,1,7776,6,6,1,36,1,6,6,216,1,6,1,36,36,6,1,1296,1,6,6,36,1,216,
%U A244416 1,216,6,6,1,36,1,6,36,46656,1,6,1,36,6,6,1,216,1,6,6,36,1,6,1,1296,1296,6,1,36,1,6
%N A244416 6-adic value of 1/n for n >= 1.
%C A244416 For the definition of 'g-adic value of x', called |x|_g with g an integer >= 2, see the Mahler reference, p. 7. Sometimes also called g-adic absolute value of x. If g is not a prime then this is called a non-archimeden pseudo-valuation. See Mahler, p. 10.
%D A244416 Kurt Mahler, p-adic numbers and their functions, second ed., Cambridge University Press, 1981.
%F A244416 a(n) = 1 if n == 1 or 5 (mod 6). a(n) = 6^max(A007814(n), A007949(n)) if n == 0 (mod 6), a(n) = 6^A007814(n) if n == 2 or 4 (mod 6), a(n) = 6^A007949(n) if n == 3 (mod 6). The exponents, called f(1/n) in the Mahler reference, are given in A244417(n).
%F A244416 a(n) = 6^A244417(n). - _Amiram Eldar_, Aug 19 2024
%e A244416 a(6) = 6^max(1,1) = 6^1 = 6. a(12) = 6^max(2,1) = 6^2 = 36,
%e A244416 a(18) = 6^max(1,2) = 36, a(24) = 6^max(3,1) = 6^3 = 216, ...
%e A244416 a(2) = 6^1 = 6, a(8) = 6^3 = 216, a(14) = 6^1 = 6, ...
%e A244416 a(3) = 6^1 = 6, a(9) = 6^2 = 36, a(15) = 6^1 = 6, ...
%e A244416 a(4) = 6^2 = 36, a(10) = 6^1 = 6, a(16) = 6^4 = 1296, ...
%t A244416 a[n_] := 6^Max[IntegerExponent[n, {2, 3}]]; Array[a, 100] (* _Amiram Eldar_, Aug 19 2024 *)
%o A244416 (PARI) a(n) = 6^max(valuation(n, 2), valuation(n, 3)); \\ _Amiram Eldar_, Aug 19 2024
%Y A244416 Cf. A244417, A006519 (g=2), A038500 (g=3), A240226 (g=4), A060904 (g=5).
%K A244416 nonn,easy
%O A244416 1,2
%A A244416 _Wolfdieter Lang_, Jun 30 2014