A065884 a(n) = A065824(A047845(n+1)).

323, 899, 1763, 5249, 3239, 979801, 5459, 10763, 9179, 9701, 10403, 12319, 5646547, 24569, 19109, 19043, 22499, 50819, 41309, 32639, 46979, 34579, 39059, 125969, 49769, 49949, 154559, 48554797, 114953, 52532203, 56624063, 195499, 75077, 79799, 72899

Offset: 1

Author

Labos Elemer, Nov 27 2001

Keywords

• nonn

Comments

By definition (m+1)*phi(a(n)) = m*sigma(a(n)) where m=A065824(n+1).

Examples

			A065824(4) = 323, so a(1) = A065824[A047845(1+1)] = 323 A065824(16) = 979801 and a(6) = 979801 = A065824[A047845(1+6)]
		

Crossrefs

Cf. A065824, A047845, A000010, A000203.

Programs

Python

from math import prod
from itertools import count
from sympy import factorint, primepi
def A065884(n):
    m, k = n, primepi(n+1) + n + (n+1>>1)
    while m != k:
        m, k = k, primepi(k) + n + (k>>1)
    m = m-1>>1
    for k in count(1):
        f = factorint(k)
        if (m+1)*k*prod((p-1)**2 for p in f)==m*prod(p**(e+2)-p for p,e in f.items()):
            return k # Chai Wah Wu, Aug 12 2024

Extensions

Name corrected and more terms from Sean A. Irvine, Sep 17 2023