A097211 a(n) = the number of sets of distinct positive integers with a least common multiple of A025487(n), i.e., A076078(A025487(n)).

1, 2, 4, 10, 8, 44, 16, 184, 218, 32, 400, 752, 3748, 64, 3392, 3040, 61064, 128, 27904, 253808, 12224, 64594, 57856, 981520, 256, 226304, 16450240, 49024, 16700300, 954368, 15722528, 512, 1822720, 1055953664, 196352, 4278006328, 15499264

Offset

1,2

Comments

The sequence A025487 contains the least number of each prime signature.

Sequence is a rearrangement of A097210 unless two or more members of A025487 are LCMs of an identical number of sets of distinct positive integers.

Links

Amiram Eldar, Table of n, a(n) for n = 1..2534

Mathematica

f[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu[n/d](2^DivisorSigma[0, d] - 1))]; PrimeExponents[n_] := Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[n]]; lpe = {}; ln = {1}; Do[pe = Sort[PrimeExponents[n]]; If[ Position[lpe, pe] == {}, AppendTo[lpe, pe]; AppendTo[ln, f[n]]], {n, 1000}]; ln (* Robert G. Wilson v, Aug 14 2004 *)

Prog

(Python)
from functools import lru_cache
from itertools import count
from sympy import prime, integer_log, primorial, mobius, divisor_count, divisors
from oeis_sequences.OEISsequences import bisection
def A097211(n):
    if n == 1: return 1
    @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 = n-1+x
        for k in count(1):
            if primorial(k)>x:
                break
            c -= g(x, k, 1)
        return c
    m = bisection(f, n, n)
    return sum(mobius(m//d)<<divisor_count(d) for d in divisors(m, generator=True)) # Chai Wah Wu, Mar 24 2026

Crossrefs

Cf. A025487, A076078, A097210.

Sequence in context: A124108 A173824 A356603 * A092945 A320150 A056376

Adjacent sequences: A097208 A097209 A097210 * A097212 A097213 A097214

Keyword

nonn

Author

Matthew Vandermast, Aug 09 2004

Extensions

Second comment edited by Matthew Vandermast, Oct 21 2008

Status

approved