A158341 a(n) = A013928(A002110(n)).

0, 1, 4, 18, 128, 1404, 18261, 310346, 5896727, 135624239, 3933101823, 121926157640, 4511267827531, 184961980943492, 7953365180610400, 373808163488684049, 19811832664899731265, 1168898127229083969892

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = -1 + Sum_{i=1..floor(sqrt(A002110(n)))} moebius(i)*floor(A002110(n)/i^2). - Jinyuan Wang, Jan 24 2025

Mathematica

Table[-1 + Sum[MoebiusMu[k]*Floor[#/(k^2)], {k, Floor[Sqrt[#]]}] &[Product[Prime[i], {i, n}]], {n, 0, 12}] (* Michael De Vlieger, Jan 24 2025 *)

Prog

(PARI) a(n) = my(t=vecprod(primes(n))-1); sum(i=1, sqrtint(t), t\i^2*moebius(i)); \\ Jinyuan Wang, Jan 24 2025
(Python)
from math import isqrt
from sympy import primorial, mobius
def A158341(n):
    if n == 0: return 0
    m = primorial(n)-1
    return sum(mobius(k)*(m//k**2) for k in range(1, isqrt(m)+1)) # Chai Wah Wu, Jan 25 2025

Crossrefs

Cf. A002110, A013928, A071172, A143658, A380403.

Sequence in context: A001423 A308351 A291335 * A144272 A034517 A294462

Adjacent sequences: A158338 A158339 A158340 * A158342 A158343 A158344

Keyword

nonn,more,changed

Author

Mats Granvik, Mar 16 2009

Extensions

Extended and offset corrected by Max Alekseyev, Sep 13 2009

a(15) from Michael De Vlieger, Jan 24 2025

a(16)-a(17) from Chai Wah Wu, Jan 25 2025

Status

approved