A365804 -id:A365804 - cp's OEIS frontend

A365712 Sum of balanced ternary enumeration of integers (A117966) and its Dirichlet inverse.

2, 0, 0, 1, 0, -6, 0, -7, 9, -4, 0, 21, 0, 4, 12, 13, 0, -9, 0, -10, -12, -16, 0, -3, 4, -26, 27, -32, 0, 72, 0, -1, 48, -10, -8, 36, 0, 16, 78, 94, 0, 54, 0, 50, 18, 14, 0, 3, 4, 74, 30, 91, 0, -27, 32, -25, -48, -52, 0, -30, 0, -62, -18, -74, 52, 18, 0, -25, -42, -66, 0, -36, 0, -74, -78, -110, -32, 0, 0, -40, 81

Offset: 1

Antti Karttunen, Sep 19 2023

sign

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

Cf. A117966, A365711.

Cf. also A365714, A365804.

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)));
A365712(n) = (A117966(n)+A365711(n));

a(n) = A117966(n) + A365711(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A117966(d) * A365711(n/d).

A365803 Dirichlet inverse of bijective base-3 reverse of n (A263273).

Original entry on oeis.org

1, -2, -3, 0, -7, 6, -5, 0, 0, 18, -19, 0, -13, -2, 21, 0, -25, 0, -11, -8, 15, 62, -23, 0, 32, 26, 0, 40, -55, -54, -37, -32, 57, 54, -3, 0, -31, -14, 39, 0, -67, 6, -49, -96, 0, 58, -61, 0, -18, -156, 75, 0, -79, 0, 237, -32, 33, 182, -65, 24, -47, 74, 0, 160, 123, -186, -41, 16, 69, 230, -77, 0, -35, 62, -96, 144

Offset: 1

Antti Karttunen, Sep 19 2023

sign

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

Cf. A263273, A323239 (parity of terms), A365804.

Cf. also A365711.

A030102(n) = { my(r=[n%3]); while(0A263273 = n -> if(!n,n,A030102(n/(3^valuation(n,3))) * (3^valuation(n, 3)));
memoA365803 = Map();
A365803(n) = if(1==n,1,my(v); if(mapisdefined(memoA365803,n,&v), v, v = -sumdiv(n,d,if(dA263273(n/d)*A365803(d),0)); mapput(memoA365803,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA263273(n/d) * a(d).

cp's OEIS Frontend

A365712 Sum of balanced ternary enumeration of integers (A117966) and its Dirichlet inverse.

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