A181820 - OEIS

A181820

a(1) = 1; for n > 1, if A025487(n) = Product p(i)^e(i), then a(n) = Product p(e(i)).

1, 2, 3, 4, 5, 6, 7, 10, 8, 11, 9, 14, 12, 13, 15, 22, 20, 17, 21, 18, 26, 16, 25, 28, 19, 33, 30, 34, 24, 35, 44, 23, 39, 42, 38, 40, 55, 27, 52, 29, 50, 51, 36, 49, 66, 46, 56, 65, 45, 68, 31, 70, 57, 32, 60, 77, 78, 58, 88, 85, 63, 76, 37, 110, 69, 48, 84, 91, 75, 102, 62, 54, 98, 104, 95

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OFFSET

1,2

COMMENTS

A permutation of the positive integers.

The partition given by the prime signature of A025487(n) has Heinz number a(n). - Pontus von Brömssen, Mar 25 2023

LINKS

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

Index entries for sequences that are permutations of the positive integers

FORMULA

a(n) = A181819(A025487(n)).

a(n) = A122111(A181815(n)).

EXAMPLE

A025487(8) = 24 = 2^3*3 has the exponents (3,1) in its canonical prime factorization. Accordingly, a(8) = prime(3)*prime(1) (i.e., A000040(3)*A000040(1)), which equals 5*2=10.

PROG

(Python)

from math import prod

from itertools import count

from functools import lru_cache

from sympy import prime, integer_log, factorint

from oeis_sequences.OEISsequences import bisection

def A181820(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)

def f(x):

c, p = n-1+x, 1

for k in count(1):

p *= prime(k)

if p>x:

break

c -= g(x, k, 1)

return c

return prod(prime(e) for e in factorint(bisection(f, n, n)).values()) # Chai Wah Wu, Mar 30 2026

CROSSREFS

A181815 is another mapping from the members of A025487 to the positive integers. Also see A181819, A181821.

Cf. A000040, A122111, A361808 (inverse), A361809 (fixed points).

Sequence in context: A368431 A194963 A072794 * A371249 A354369 A199426

Adjacent sequences: A181817 A181818 A181819 * A181821 A181822 A181823

KEYWORD

nonn,changed

AUTHOR

Matthew Vandermast, Dec 07 2010

STATUS

approved