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A323900
Sum of A287896 and its Dirichlet inverse.
2
2, 0, 0, 4, 0, 8, 0, 4, 4, 12, 0, 4, 0, 12, 12, 5, 0, 8, 0, 6, 12, 20, 0, 8, 9, 20, 8, 6, 0, -8, 0, 6, 20, 20, 18, 12, 0, 28, 20, 12, 0, 8, 0, 10, 4, 28, 0, 10, 9, 10, 20, 10, 0, 16, 30, 12, 28, 28, 0, 20, 0, 20, 20, 7, 30, -16, 0, 10, 28, 0, 0, 16, 0, 44, -2, 14, 30, 0, 0, 15, 16, 44, 0, 28, 30, 52, 28, 20, 0, 40
OFFSET
1,1
LINKS
FORMULA
a(n) = A287896(n) + A323899(n).
PROG
(PARI)
up_to = 20000;
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A001511(n) = (1+valuation(n, 2));
A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
A287896(n) = (A001511(n)*A002487(n));
v323899 = DirInverse(vector(up_to, n, A287896(n)));
A323899(n) = v323899[n];
A323900(n) = (A287896(n)+A323899(n));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Feb 12 2019
STATUS
approved