A389958 Odd perfect powers (not including 1) plus 1.

10, 26, 28, 50, 82, 122, 126, 170, 226, 244, 290, 344, 362, 442, 530, 626, 730, 842, 962, 1090, 1226, 1332, 1370, 1522, 1682, 1850, 2026, 2188, 2198, 2210, 2402, 2602, 2810, 3026, 3126, 3250, 3376, 3482, 3722, 3970, 4226, 4490, 4762, 4914, 5042, 5330, 5626, 5930

Offset

1,1

Links

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

Formula

a(n) = A075109(n+1) + 1.

a(n) = A389764(n) + 2.

a(n) = A389955(n) / A389765(n).

Sum_{n>=1} 1/a(n) = 1 - log(2) - (10 - Pi^2)/4 = A244009 - A348670 / 4.

Mathematica

seq[lim_] := Union[Table[m^k + 1, {k, 2, Log2[lim]}, {m, 3, Surd[lim, k], 2}] // Flatten]; seq[6000]

Prog

(PARI) list(lim) = {my(s = List()); for(k = 2, logint(lim, 2), forstep(m = 3, sqrtnint(lim, k), 2, listput(s, m^k + 1))); Set(s); }
(Python)
from sympy import mobius, integer_nthroot
from oeis_sequences.OEISsequences import bisection
def A389958(n): return bisection(lambda x:int(n+x+sum(mobius(k)*((integer_nthroot(x-1, k)[0]+1>>1)-1) for k in range(2, (x-1).bit_length()))), n, n) # Chai Wah Wu, Oct 21 2025

Crossrefs

Intersection of A005843 and A216765.

Complement of A389957 within A216765.

Cf. A075109, A244009, A348670, A389764, A389765, A389955.

Sequence in context: A059198 A259297 A358774 * A046961 A246826 A125035

Adjacent sequences: A389955 A389956 A389957 * A389959 A389960 A389961

Keyword

nonn,easy

Author

Amiram Eldar, Oct 20 2025

Status

approved