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

Author

Henry Bottomley, Mar 28 2000

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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

Formula

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

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

Extensions

More terms from David Wasserman, Feb 17 2006

Offset corrected by Amiram Eldar, Nov 21 2020