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A285720
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Number of ways to write n as a sum of two unordered squarefree numbers so that their addition in base-2 does not produce carries.
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2
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0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 5, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 3, 0, 0, 0, 6, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 11, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 3, 0, 0, 0, 11, 0, 0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 7, 0, 0, 0, 13, 0, 0, 0, 3, 0, 0, 0, 9, 0
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OFFSET
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1,7
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LINKS
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FORMULA
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a(n) = sum(i=1..floor(n/2), abs(mu(i)*mu(n-i))*[A003987(i,n-i) == n]. (Here [] is Iverson bracket, giving in this case 1 only if (i XOR (n-i)) is equal to n, and 0 otherwise. mu is Moebius mu function, A008683.)
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MATHEMATICA
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Table[Sum[Abs[MoebiusMu[i] MoebiusMu[n - i]] Boole[BitXor[i, n - i] == n], {i, Floor[n/2]}], {n, 120}] (* Michael De Vlieger, May 03 2017 *)
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PROG
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(Python)
from sympy import mobius
def a003987(n, i): return i^(n - i) == n
def a(n): return sum([abs(mobius(i)*mobius(n - i))*(1*a003987(n, i)) for i in range(1, n//2 + 1)])
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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