A346043 a(n) is the position of A138534(n) in A025487.

1, 2, 6, 17, 67, 166, 676, 1373, 4475, 10446, 30036, 51032, 196386, 315302, 737515, 1654229, 4227565, 6301902, 17975187, 26010425, 70085244, 133337963, 250039913, 346136188, 1096793068, 1711865265, 3030290770, 5257516008, 11602637216, 15293266726, 41896261337

Offset

0,2

Links

Chai Wah Wu, Table of n, a(n) for n = 0..36

Formula

A025487(a(n)) = A138534(n).

Example

A138534(2) = A025487(6) = 12, so a(2) = 6.

Mathematica

lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; s = {}; Do[p = Position[lps, Product[Prime[k]^Floor[n/k], {k, 1, n}]]; If[p == {}, Break[]]; AppendTo[s, p[[1, 1]]], {n, 0, 20}]; s

Prog

(PARI) f(m) = my(c=1, p, q=2, v=vector(logint(m, 2), i, 2^i), w); while(#v, c+=#v; p=q; q=nextprime(q+1); w=List([]); for(i=1, #v, for(j=1, min(valuation(v[i], p), logint(m\v[i], q)), listput(w, v[i]*q^j))); v=w); c;
a(n) = f(prod(k=1, n, prime(k)^(n\k))); \\ Jinyuan Wang, Jul 08 2021
(Python)
from math import prod
from itertools import count
from functools import lru_cache
from sympy import prime, integer_log, primorial
def A346043(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)
    c, f = 1, prod(prime(k)**(n//k) for k in range(1, n+1))
    for k in count(1):
        if primorial(k)>f:
            break
        c += g(f, k, 1)
    return c # Chai Wah Wu, Mar 23 2026

Crossrefs

Cf. A025487, A138534.

Similar sequences: A098718, A098719, A293635, A306802.

Sequence in context: A150038 A150039 A150040 * A079456 A264761 A253882

Adjacent sequences: A346040 A346041 A346042 * A346044 A346045 A346046

Keyword

nonn,more

Author

Amiram Eldar, Jul 02 2021

Extensions

a(20)-a(21) from Jinyuan Wang, Jul 08 2021

a(22)-a(30) from Chai Wah Wu, Mar 23 2026

Status

approved