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A053811
Primes (in order) occurring in A053810.
4
2, 2, 3, 5, 3, 2, 7, 11, 5, 2, 13, 3, 17, 7, 19, 23, 29, 31, 11, 37, 41, 43, 2, 3, 13, 47, 53, 5, 59, 61, 67, 17, 71, 73, 79, 19, 83, 89, 2, 97, 101, 103, 107, 109, 23, 113, 127, 7, 131, 137, 139, 149, 151, 29, 157, 163, 167, 31, 173, 179, 181, 191, 193, 197, 199, 211, 223
OFFSET
1,1
LINKS
FORMULA
a(n) = A006530(A053810(n)) = A020639(A053810(n)). - David Wasserman, Feb 17 2006
a(n) = A053810(n)^(1/A053812(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])); A = vector(count); for (i = 1, count, f = factor(v[i]); A[i] = f[1, 1]); A \\ David Wasserman, Feb 17 2006
(Python)
from sympy import primepi, integer_nthroot, primerange, primefactors
def A053811(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 primefactors(kmax)[0] # Chai Wah Wu, Aug 13 2024
KEYWORD
easy,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