A053812 Exponents occurring in A053810.

2, 3, 2, 2, 3, 5, 2, 2, 3, 7, 2, 5, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 11, 7, 3, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 13, 2, 2, 2, 2, 2, 3, 2, 2, 5, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 7, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 17, 2, 2, 2, 2, 3, 2, 2, 2

Offset

1,1

Links

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

Formula

a(n) = A001222(A053810(n)). - David Wasserman, Feb 17 2006

a(n) = log(A053810(n))/log(A053811(n)). - Amiram Eldar, Nov 21 2020

Prog

(PARI) LIM = prime(80)^2; v = vector(400); count = 0; forprime (p = 2, prime(80), x = 2; while (p^x <= LIM, count++; v[count] = p^x; x = nextprime(x + 1))); v = vecsort(vector(count, i, v[i])); vector(count, i, bigomega(v[i])) \\ David Wasserman, Feb 17 2006
(Python)
from sympy import primepi, integer_nthroot, primerange, factorint
def A053812(n):
    def f(x): return int(n-1+x-sum(primepi(integer_nthroot(x, p)[0]) for p in primerange(x.bit_length())))
    kmin, kmax = 1, 2
    while f(kmax) >= kmax:
        kmax <<= 1
    while True:
        kmid = kmax+kmin>>1
        if f(kmid) < kmid:
            kmax = kmid
        else:
            kmin = kmid
        if kmax-kmin <= 1:
            break
    return list(factorint(kmax).values())[0] # Chai Wah Wu, Aug 13 2024

Crossrefs

Cf. A000961, A000961, A001222, A025473, A053810, A053811.

Sequence in context: A358640 A096258 A049879 * A177865 A307835 A341651

Adjacent sequences: A053809 A053810 A053811 * A053813 A053814 A053815

Keyword

nonn

Author

Henry Bottomley, Mar 28 2000

Extensions

More terms from David Wasserman, Feb 17 2006

Offset corrected by Amiram Eldar, Nov 21 2020

Status

approved