A393258 a(n) is the position of A003961(A025487(n)) in A147516.

1, 2, 3, 4, 5, 6, 7, 9, 8, 11, 10, 13, 12, 15, 14, 18, 16, 21, 20, 19, 25, 17, 23, 22, 28, 27, 26, 32, 24, 30, 29, 38, 37, 34, 43, 31, 41, 33, 40, 50, 39, 49, 36, 47, 45, 55, 42, 53, 44, 52, 64, 51, 62, 35, 48, 60, 58, 72, 54, 70, 56, 67, 82, 65, 80, 46, 61, 78, 63, 76, 91, 57, 74, 71, 89, 73, 69, 85, 86, 104

Offset

1,2

Comments

This is a permutation of the positive integers.

Links

Table of n, a(n) for n=1..80.

Index entries for sequences that are permutations of the natural numbers.

Example

a(11) = 10 as A025487(11) = 36 = 2^2 * 3^2. When replacing each prime factor in the prime factorization with the next larger prime we get 3^3 * 5^2 = 225 = A147516(10).

Prog

(Python)
from functools import lru_cache
from itertools import count
from sympy import prime, integer_log, primorial, nextprime, factorint
from oeis_sequences.OEISsequences import bisection
def A393258(n):
    @lru_cache(maxsize=None)
    def g(x, m, j): return sum(g(x//(prime(m)**i), m-1, i) for i in range(j, integer_log(x, prime(m))[0]+1)) if m-1 else max(0, x.bit_length()-j)
    @lru_cache(maxsize=None)
    def h(x, m, j): return sum(h(x//(prime(m)**i), m-1, i) for i in range(j, integer_log(x, prime(m))[0]+1)) if m>2 else max(0, integer_log(x, 3)[0]+1-j)
    def f(x):
        c = n-1+x
        for k in count(1):
            if primorial(k)>x:
                break
            c -= g(x, k, 1)
        return c
    m, c = prod(nextprime(p)**e for p, e in factorint(bisection(f, n, n)).items()), 1
    for k in count(2):
        if primorial(k)>(m<<1):
            break
        c += h(m, k, 1)
    return c # Chai Wah Wu, Mar 23 2026

Crossrefs

Cf. A003961, A025487, A147516.

Sequence in context: A294660 A180198 A180199 * A284120 A183081 A140595

Adjacent sequences: A393255 A393256 A393257 * A393259 A393260 A393261

Keyword

nonn

Author

David A. Corneth, Feb 07 2026

Status

approved