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A107079
Minimal number of squared primes in a squarefree gap of length n.
4
1, 2, 3, 4, 4, 5, 6, 7, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 17, 18, 18, 18, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 30, 30, 31, 32, 32, 32, 32, 33, 33, 34, 34, 35, 35, 36, 37, 38, 38, 39, 40, 40, 40, 41, 42, 43, 43, 44, 45, 46, 46, 47
OFFSET
1,2
FORMULA
a(n) = sum{k=0..n-1, moebius_mu(n-k-1) mod 2}.
a(n) = A013928(n+1) + A107078(n).
From Antti Karttunen, Oct 07 2016: (Start)
a(n) = 1 + A013928(n). [Cf. Charles R Greathouse IV's PARI-program.]
For all n >= 1, a(A005117(n)) = n.
(End)
MATHEMATICA
a[n_] := Sum[Boole[SquareFreeQ[k]], {k, 1, n-1}] + 1;
Array[a, 100] (* Jean-François Alcover, Sep 11 2018, from A013928 *)
PROG
(PARI) A107079(n)=1+sum(k=1, n-1, bitand(moebius(k), 1)) \\ Charles R Greathouse IV, Sep 22 2008
(Python)
from math import isqrt
from sympy import mobius
def A107079(n): return 1+sum(mobius(k)*((n-1)//k**2) for k in range(1, isqrt(n-1)+1)) # Chai Wah Wu, Jan 03 2024
CROSSREFS
One more than A013928. A left inverse of A005117.
Sequence in context: A306890 A116549 A268382 * A025528 A255338 A123580
KEYWORD
nonn
AUTHOR
Paul Barry, May 10 2005
EXTENSIONS
New definition from Charles R Greathouse IV, Sep 22 2008
STATUS
approved