A365713 -id:A365713 - cp's OEIS frontend

A365711 Dirichlet inverse of balanced ternary enumeration of integers (A117966).

1, 1, -3, -3, -2, -3, 2, -3, 0, -14, -8, 9, -13, -7, 6, 6, -5, 0, 8, 0, -6, -11, 7, 9, 15, -13, 0, -60, -26, 42, -31, -30, 24, -35, -31, 0, -37, -19, 39, 54, -38, 21, -34, 18, 0, -5, -17, -18, -18, 54, 15, 75, -14, 0, 58, 3, -24, -29, 25, 0, 29, -31, 0, -57, 71, 33, 14, -9, -21, -46, 22, 0, 35, -37, -45, -78, 2, 39

Offset: 1

Antti Karttunen, Sep 19 2023

sign

Antti Karttunen, Table of n, a(n) for n = 1..19683

Cf. A011655, A117966, A359377, A365428, A365712.

Cf. also A365713, A365803.

A117966(n) = subst(Pol(apply(x->if(x == 2, -1, x), digits(n, 3)), 'x), 'x, 3); \\ From A117966 by Gheorghe Coserea
memoA365711 = Map();
A365711(n) = if(1==n,1,my(v); if(mapisdefined(memoA365711,n,&v), v, v = -sumdiv(n,d,if(dA117966(n/d)*A365711(d),0)); mapput(memoA365711,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA117966(n/d) * a(d).

A011655(abs(a(n))) = A359377(n).

A365714 Sum of reversing binary value of n (A065620) and its Dirichlet inverse.

Original entry on oeis.org

2, 0, 0, 4, 0, -4, 0, 8, 1, -12, 0, -4, 0, 12, 6, 16, 0, -30, 0, -12, -6, 28, 0, -8, 9, 20, 15, 12, 0, -32, 0, 32, -14, -60, -18, -28, 0, 60, -10, -24, 0, 64, 0, 28, 61, -52, 0, -16, 9, 18, 30, 20, 0, -66, -42, 24, -30, -44, 0, -20, 0, 44, -77, 64, -30, -96, 0, -60, 26, 160, 0, -56, 0, 116, 39, 60, 42, -96, 0, -48, 89

Offset: 1

Antti Karttunen, Sep 19 2023

sign

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A065620, A365713.

Cf. also A365712.

A065620(n, c=1) = sum(i=0, logint(n+!n, 2), if(bittest(n, i), (-1)^c++<A065620 by M. F. Hasler
memoA365713 = Map();
A365713(n) = if(1==n,1,my(v); if(mapisdefined(memoA365713,n,&v), v, v = -sumdiv(n,d,if(dA065620(n/d)*A365713(d),0)); mapput(memoA365713,n,v); (v)));
A365714(n) = (A065620(n)+A365713(n));

a(n) = A065620(n) + A365713(n).
a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A065620(d) * A365713(n/d).
a(4*n)/4 = A065620(n).

cp's OEIS Frontend

A365711 Dirichlet inverse of balanced ternary enumeration of integers (A117966).

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