A143519 Moebius transform of A010051, the characteristic function of the primes: a(n) = Sum_{d|n} mu(n/d)*A010051(d); A054525 * A010051.
0, 1, 1, -1, 1, -2, 1, 0, -1, -2, 1, 1, 1, -2, -2, 0, 1, 1, 1, 1, -2, -2, 1, 0, -1, -2, 0, 1, 1, 3, 1, 0, -2, -2, -2, 0, 1, -2, -2, 0, 1, 3, 1, 1, 1, -2, 1, 0, -1, 1, -2, 1, 1, 0, -2, 0, -2, -2, 1, -1, 1, -2, 1, 0, -2, 3, 1, 1, -2, 3, 1, 0, 1, -2, 1, 1, -2, 3, 1, 0, 0, -2, 1, -1, -2, -2, -2, 0, 1
Offset: 1
Keywords
Examples
a(4) = -1 since row 4 of triangle A043518 = (0, -1, 0, 0). a(4) = -1 = (0, -1, 0, 1) dot (0, 1, 1, 0), where (0, -1, 0, 1) = row 4 of A054525 and A010051 = (0, 1, 1, 0, 1, 0, 1, 0, ...).
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[Sum[MoebiusMu[n/d] Boole[PrimeQ@ d], {d, Divisors@ n}], {n, 89}] (* Michael De Vlieger, Jul 19 2017 *) -
PARI
A143519(n) = sumdiv(n,d,isprime(d)*moebius(n/d)); \\ (After Luschny's Sage-code) - Antti Karttunen, Jul 19 2017
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Sage
def A143519(n) : D = filter(is_prime, divisors(n)) return add(moebius(n/d) for d in D) [A143519(n) for n in (1..89)] # Peter Luschny, Feb 01 2012
Formula
Mobius transform of A010051, the characteristic function of the primes.
Row sums of triangle A143518.
a(n) = Sum_{a*b*c=n} omega(a)*mu(b)*mu(c). - Benedict W. J. Irwin, Mar 02 2022
Extensions
More terms from R. J. Mathar, Jan 19 2009
Comments