A354925 Union of powers of primes and even semiprimes.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 26, 27, 29, 31, 32, 34, 37, 38, 41, 43, 46, 47, 49, 53, 58, 59, 61, 62, 64, 67, 71, 73, 74, 79, 81, 82, 83, 86, 89, 94, 97, 101, 103, 106, 107, 109, 113, 118, 121, 122, 125, 127, 128, 131, 134, 137, 139, 142, 146, 149, 151, 157, 158, 163, 166, 167, 169

Offset

1,2

Links

Table of n, a(n) for n=1..76.

Mathematica

Join[{1}, Select[Range[170], PrimePowerQ[#] || PrimeQ[#/2] &]] (* Amiram Eldar, Jun 13 2022 *)

Prog

(PARI)
A354923(n) = ((1==n)|| isprimepower(n) || (!(n%2) && isprime(n/2)));
isA354925(n) = A354923(n);
(Python)
from sympy import primepi, integer_nthroot
from oeis_sequences.OEISsequences import bisection
def A354925(n):
    def f(x): return int(n+x-1-sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, x.bit_length()))-primepi(x>>1))+(x>=4)
    return bisection(f, n, n) # Chai Wah Wu, Jun 09 2026

Crossrefs

Union of A000961 and A100484.

Apart from {1}, complement of A265128.

Cf. A354923 (characteristic function).

Sequence in context: A195044 A033112 A049813 * A362184 A368904 A229991

Adjacent sequences: A354922 A354923 A354924 * A354926 A354927 A354928

Keyword

nonn,changed

Author

Antti Karttunen, Jun 13 2022

Status

approved