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A371638
a(n) = 2*n + valuation(n, 3) with valuation(n, 3) = A007949(n).
3
2, 4, 7, 8, 10, 13, 14, 16, 20, 20, 22, 25, 26, 28, 31, 32, 34, 38, 38, 40, 43, 44, 46, 49, 50, 52, 57, 56, 58, 61, 62, 64, 67, 68, 70, 74, 74, 76, 79, 80, 82, 85, 86, 88, 92, 92, 94, 97, 98, 100, 103, 104, 106, 111, 110, 112, 115, 116, 118, 121, 122, 124, 128, 128
OFFSET
1,1
COMMENTS
See A371639 for the connection with Voronoi's congruence.
FORMULA
a(n) = valuation(denominator(Voronoi(3, n))) where Voronoi(c, n) = ((c^n - 1) * bernoulli(n)) / (n * c^(n - 1)).
MAPLE
A371638 := n -> 2*n + padic:-ordp(n, 3): seq(A371638(n), n = 1..64);
MATHEMATICA
Array[2 # + IntegerExponent[#, 3] &, 64] (* Michael De Vlieger, Mar 31 2024 *)
PROG
(SageMath)
def A371638(n): return 2 * n + valuation(n, 3)
print([A371638(n) for n in range(1, 65)])
CROSSREFS
Cf. A007949, A371639, A292608 (c=2).
Sequence in context: A207829 A207827 A047236 * A039581 A367498 A338420
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Mar 30 2024
STATUS
approved