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A323884
Sum of A322026 and its Dirichlet inverse.
5
2, 0, 0, 4, 0, 12, 0, 8, 9, 4, 0, 8, 0, 4, 6, 8, 0, 4, 0, 4, 6, 4, 0, 0, 1, 4, 15, 4, 0, -2, 0, 12, 6, 4, 2, 13, 0, 4, 6, 4, 0, -2, 0, 4, 5, 4, 0, 22, 1, 2, 6, 4, 0, 7, 2, 4, 6, 4, 0, 8, 0, 4, 5, 20, 2, -2, 0, 4, 6, 0, 0, 38, 0, 4, 3, 4, 2, -2, 0, 10, 13, 4, 0, 8, 2, 4, 6, 4, 0, 16, 2, 4, 6, 4, 2, 28, 0, 2, 5, 4, 0, -2, 0, 4, 0
OFFSET
1,1
FORMULA
a(n) = A322026(n) + A323883(n).
PROG
(PARI)
up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
A007814(n) = valuation(n, 2);
A007949(n) = valuation(n, 3);
v322026 = rgs_transform(vector(up_to, n, [A007814(n), A007949(n)]));
A322026(n) = v322026[n];
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.
v323883 = DirInverse(v322026);
A323883(n) = v323883[n];
A323884(n) = (A322026(n)+A323883(n));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Feb 08 2019
STATUS
approved