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URL: https://oeis.org/A346407

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A346407
a(n) is the position of A051451(n) in A025487.
2
1, 2, 4, 6, 13, 29, 36, 55, 112, 223, 264, 514, 956, 1749, 2345, 2847, 5005, 8567, 9507, 16073, 26792, 43730, 70482, 88969, 140871, 221370, 342958, 368588, 565510, 859401, 1290994, 1927925, 2128165, 3142980, 4616207, 6754033, 9810997, 14133201, 20230329, 28744301
OFFSET
1,2
COMMENTS
Equivalently, the positions of the distinct terms of A003418 in A025487.
FORMULA
A025487(a(n)) = A003418(n).
EXAMPLE
A138534(1) = A025487(1) = 1, so a(1) = 1.
A138534(2) = A025487(2) = 2, so a(2) = 2.
A138534(3) = A025487(4) = 6, so a(3) = 4.
MATHEMATICA
lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; s = {}; lcms = Union @ Table[LCM @@ Range[n], {n, 1, 31}]; Do[p = Position[lps, lcms[[n]]]; If[p == {}, Break[]]; AppendTo[s, p[[1, 1]]], {n, 1, Length[lcms]}]; s
PROG
(Python)
from itertools import takewhile, count
from functools import lru_cache
from sympy import prime, integer_log, primepi, integer_nthroot, primerange, primorial
def A346407(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): return int(n+x-1-sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, x.bit_length())))
m = iterfun(f, n)
r = prod(p**integer_log(m, p)[0] for p in primerange(m+1))
return 1+sum(g(r, k, 1) for k in takewhile(lambda x:primorial(x)<=r, count(1))) # Chai Wah Wu, Mar 26 2026
CROSSREFS
Similar sequences: A098718, A098719, A293635, A306802, A346043.
Sequence in context: A105543 A309352 A295618 * A369390 A324376 A027712
KEYWORD
nonn,changed
AUTHOR
Amiram Eldar, Jul 15 2021
STATUS
approved