A365712 -id:A365712 - 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).

A365804 Sum of bijective base-3 reverse of n (A263273) and its Dirichlet inverse.

Original entry on oeis.org

2, 0, 0, 4, 0, 12, 0, 8, 9, 28, 0, 12, 0, 20, 42, 16, 0, 18, 0, 12, 30, 76, 0, 24, 49, 52, 27, 68, 0, -24, 0, 32, 114, 100, 70, 36, 0, 44, 78, 40, 0, 72, 0, -20, 63, 92, 0, 48, 25, -86, 150, 52, 0, 54, 266, 24, 66, 220, 0, 84, 0, 148, 45, 192, 182, -144, 0, 84, 138, 280, 0, 72, 0, 124, -45, 188, 190, 0, 0, 80, 81

Offset: 1

Antti Karttunen, Sep 19 2023

sign

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

Cf. A263273, A323239, A365803.

Cf. also A365712.

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)));
A365804(n) = (A263273(n)+A365803(n));

a(n) = A263273(n) + A365803(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A263273(d) * A365803(n/d).

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A365804 Sum of bijective base-3 reverse of n (A263273) and its Dirichlet inverse.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula