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a(n) = 2*n + valuation(n, 3) with valuation(n, 3) = A007949(n).
3

%I #16 Mar 31 2024 11:41:06

%S 2,4,7,8,10,13,14,16,20,20,22,25,26,28,31,32,34,38,38,40,43,44,46,49,

%T 50,52,57,56,58,61,62,64,67,68,70,74,74,76,79,80,82,85,86,88,92,92,94,

%U 97,98,100,103,104,106,111,110,112,115,116,118,121,122,124,128,128

%N a(n) = 2*n + valuation(n, 3) with valuation(n, 3) = A007949(n).

%C See A371639 for the connection with Voronoi's congruence.

%F a(n) = valuation(denominator(Voronoi(3, n))) where Voronoi(c, n) = ((c^n - 1) * bernoulli(n)) / (n * c^(n - 1)).

%p A371638 := n -> 2*n + padic:-ordp(n, 3): seq(A371638(n), n = 1..64);

%t Array[2 # + IntegerExponent[#, 3] &, 64] (* _Michael De Vlieger_, Mar 31 2024 *)

%o (SageMath)

%o def A371638(n): return 2 * n + valuation(n, 3)

%o print([A371638(n) for n in range(1, 65)])

%Y Cf. A007949, A371639, A292608 (c=2).

%K nonn,easy

%O 1,1

%A _Peter Luschny_, Mar 30 2024