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A244417 Exponents of 6 in appearing in the 6-adic value of 1/n, n>=1 (A244416).

%I A244417 #21 Aug 19 2024 12:16:12
%S A244417 0,1,1,2,0,1,0,3,2,1,0,2,0,1,1,4,0,2,0,2,1,1,0,3,0,1,3,2,0,1,0,5,1,1,
%T A244417 0,2,0,1,1,3,0,1,0,2,2,1,0,4,0,1,1,2,0,3,0,3,1,1,0,2,0,1,2,6,0,1,0,2,
%U A244417 1,1,0,3,0,1,1,2,0,1,0,4,4,1,0,2,0,1,1,3,0,2,0,2,1,1,0,5,0,1,2,2
%N A244417 Exponents of 6 in appearing in the 6-adic value of 1/n, n>=1 (A244416).
%C A244417 For the definition of 'g-dic value of 1/n' see a comment on A244416. In the Mahler reference, p. 7, the present exponent of 6 is there called f = f(1/n) for g = 6.
%D A244417 Kurt Mahler, p-adic numbers and their functions, second ed., Cambridge University Press, 1981.
%H A244417 Antti Karttunen, <a href="/A244417/b244417.txt">Table of n, a(n) for n = 1..19683</a>
%F A244417 a(n) = 0 if n is congruent 1 or 5 (mod 6). a(n) = max(A007814(n), A007949(n)) if n == 0 (mod 6). a(n) = A007814(n) if n == 2 or 4 (mod 6) and a(n) = A007949(n) if n == 3 (mod 6).
%F A244417 a(n) = max(A007814(n), A007949(n)), in all cases. - _Antti Karttunen_, Dec 04 2018
%F A244417 From _Amiram Eldar_, Aug 19 2024: (Start)
%F A244417 a(n) = A051903(A065331(n)).
%F A244417 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 13/10. (End)
%e A244417 See A244416.
%t A244417 a[n_] := Max[IntegerExponent[n, {2, 3}]]; Array[a, 100] (* _Amiram Eldar_, Aug 19 2024 *)
%o A244417 (PARI) A244417(n) = max(valuation(n,2), valuation(n,3)); \\ _Antti Karttunen_, Dec 04 2018
%Y A244417 Cf. A122841, A244416, A007814 (g=2), A007949 (g=3), A244415 (g=4), A112765 (g=5), A051903, A065331.
%Y A244417 Cf. also A322026, A322316.
%K A244417 nonn,easy
%O A244417 1,4
%A A244417 _Wolfdieter Lang_, Jul 02 2014