A365714 -id:A365714 - 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).

A365713 Dirichlet inverse of reversing binary value of n (A065620).

Original entry on oeis.org

1, -2, 1, 0, 3, -2, -3, 0, 8, -6, -7, 0, -5, 6, 11, 0, 15, -16, -15, 0, -19, 14, 13, 0, 0, 10, 24, 0, 11, -22, -11, 0, 17, -30, -49, 0, -29, 30, 19, 0, -25, 38, 25, 0, 88, -26, -27, 0, -8, 0, 47, 0, 19, -48, -61, 0, -7, -22, -23, 0, -21, 22, -56, 0, 33, -34, -63, 0, -35, 98, 61, 0, -57, 58, 96, 0, 101, -38, -59, 0

Offset: 1

Antti Karttunen, Sep 19 2023

sign

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

Cf. A065620, A365714.

Cf. also A355819, A365711.

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)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA065620(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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