A390155 Numbers of the form (3*m)^k - 1, where m >= 1 and k >= 2.

8, 26, 35, 80, 143, 215, 224, 242, 323, 440, 575, 728, 899, 1088, 1295, 1520, 1727, 1763, 2024, 2186, 2303, 2600, 2915, 3248, 3374, 3599, 3968, 4355, 4760, 5183, 5624, 5831, 6083, 6560, 7055, 7568, 7775, 8099, 8648, 9215, 9260, 9800, 10403, 11024, 11663, 12320, 12995

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Junesang Choi, Multiple gamma functions and their applications, in: G. Milovanović and M. Rassias (eds.), Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava, Springer New York, 2014, pp. 93-129. See section 5.1, p. 118.

Junesang Choi and Hari M. Srivastava, Series Involving the Zeta Functions and a Family of Generalized Goldbach-Euler Series, American Mathematical Monthly, Vol. 121, No. 3 (2014), pp. 229-236.

Formula

a(n) = A353238(n) - 1.

Sum_{n>=1} 1/a(n) = log(3)/2 - sqrt(3)*Pi/18 = A384683 = 0.2470062... .

Mathematica

seq[lim_] := Union[Table[m^k - 1, {k, 2, Log2[lim + 1]}, {m, 3, Surd[lim + 1, k], 3}] // Flatten]; seq[13000]

Prog

(PARI) list(lim) = {my(s = List());  for(k = 2, logint(lim+1, 2), forstep(m = 3, sqrtnint(lim+1, k), 3, listput(s, m^k - 1))); Set(s); }
(Python)
from sympy import mobius, integer_nthroot, integer_log
from oeis_sequences.OEISsequences import bisection
def A390155(n):
    def f(x): return n+x+sum(mobius(k)*(integer_nthroot(x+1, k)[0]//3) for k in range(2, integer_log(x+1, 3)[0]+1))
    return bisection(f, n, n) # Chai Wah Wu, Oct 31 2025

Crossrefs

Intersection of A016789 and A045542.

Complement of the disjoint union of A390156 and A390157 within A045542.

Cf. A001597, A353238, A384683, A389764, A389765.

Sequence in context: A345205 A063560 A265104 * A328205 A304910 A271989

Adjacent sequences: A390152 A390153 A390154 * A390156 A390157 A390158

Keyword

nonn,easy

Author

Amiram Eldar, Oct 27 2025

Status

approved