A024621 Positions of nonprimes among the powers of primes (A000961).

1, 4, 7, 8, 11, 15, 16, 19, 24, 28, 33, 42, 43, 45, 54, 69, 71, 79, 87, 92, 118, 121, 137, 153, 171, 188, 199, 245, 248, 293, 314, 341, 360, 361, 364, 393, 446, 483, 526, 559, 605, 651, 699, 719, 750, 857, 894, 930, 935, 1050, 1079, 1215, 1305, 1348, 1436, 1479, 1514

Offset

1,2

Links

Table of n, a(n) for n=1..57.

Prog

(PARI) lista(nn) = {vec = vector(nn, i, i); powpr = select((i->((omega(i)==1) || (i==1))), vec); for (i = 1, #powpr, if (! isprime(powpr[i]), print1(i, ", ")); ); } \\ Michel Marcus, Oct 02 2013
(Python)
from sympy import primepi, integer_nthroot
def A024621(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return int(n+x-1-sum(primepi(integer_nthroot(x, k)[0]) for k in range(2, x.bit_length())))
    return n+primepi(bisection(f, n, n)) # Chai Wah Wu, Nov 05 2024

Crossrefs

Complement of A024620.

Sequence in context: A356088 A137362 A190765 * A375572 A296029 A000606

Adjacent sequences: A024618 A024619 A024620 * A024622 A024623 A024624

Keyword

nonn

Author

Clark Kimberling

Status

approved