A300821 -id:A300821 - cp's OEIS frontend

A300822 Möbius transform of A300222.

0, 2, 0, -2, 2, 4, 6, 8, 0, -4, 2, -4, 0, -6, 4, -2, 8, 12, 18, 22, 12, 14, 20, 16, 22, 24, 0, 0, 2, -8, 0, -4, 4, -4, 0, -12, 0, -18, 0, -28, 2, -12, 6, -8, 12, -4, 20, -4, 12, -2, 16, 0, 26, 36, 50, 48, 36, 50, 56, 44, 60, 60, 36, 52, 54, 28, 54, 52, 40, 60, 62, 48, 72, 72, 44, 72, 66, 48, 78, 82, 0, -4, 2, 0, -10, -6, 4, -10, 8, -24, -6, -14, 0

Offset: 1

Antti Karttunen, Mar 14 2018

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000010, A300222, A300821, A300824.

Table[DivisorSum[n, MoebiusMu[n/#] FromDigits[IntegerDigits[#, 3] /. 1 -> 0, 3] &], {n, 93}] (* Michael De Vlieger, Mar 17 2018 *)

A300222(n) = fromdigits(apply(x->(if (1==x, 0, x)), digits(n, 3)), 3);
A300822(n) = sumdiv(n,d,moebius(n/d)*A300222(d));

a(n) = Sum_{d|n} moebius(n/d)*A300222(d).
a(n) = A000010(n) - A300821(n).
a(n) = A300222(n) - A300824(n).

A300823 Difference between A244042 and its Möbius transform.

Original entry on oeis.org

0, 1, 1, 0, 1, 2, 1, 4, 3, 2, 1, 4, 1, 0, 5, 0, 1, 6, 1, 14, 3, 8, 1, 8, 3, 12, 9, 16, 1, 14, 1, 10, 11, 8, 3, 12, 1, 0, 15, -4, 1, 12, 1, 8, 15, 2, 1, 10, 1, 8, 11, 4, 1, 18, 11, 24, 3, 26, 1, 28, 1, 30, 9, 30, 15, 20, 1, 32, 5, 46, 1, 24, 1, 36, 7, 40, 9, 24, 1, 50, 27, 38, 1, 60, 11, 36, 29, 32, 1, 42, 13, 32, 33, 26, 3, 50, 1

Offset: 1

Antti Karttunen, Mar 14 2018

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A008683, A051953, A244042, A300821, A300824, A300825.

f[n_] := FromDigits[IntegerDigits[n, 3] /. 2 -> 0, 3]; Table[f@ n - DivisorSum[n, MoebiusMu[n/#] f@ # &], {n, 97}] (* Michael De Vlieger, Mar 17 2018 *)

A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);
A300823(n) = -sumdiv(n,d,(dA244042(d));

a(n) = A244042(n) - A300821(n).
a(n) = -Sum_{d|n, dA008683(n/d)*A244042(d) = Sum_{d|n, dA300821(d).
a(n) = A051953(n) - A300824(n).

A359601 Dirichlet inverse of A244042, where A244042(n) replaces 2's with 0's in the ternary representation of n.

Original entry on oeis.org

1, 0, -3, -4, -3, 0, -1, 0, 0, -10, -9, 12, -13, -12, 9, 6, -9, 0, -1, 24, 3, -4, -3, 0, 8, 0, 0, -20, -27, 30, -31, -30, 27, -28, -21, 0, -37, -36, 39, 40, -39, 36, -37, 36, 0, -28, -27, -18, -30, 30, 27, 76, -27, 0, 53, 96, 3, -4, -3, -72, -1, 0, 0, 6, 69, 12, -13, 60, 9, 82, -9, 0, -1, 0, -24, 4, 15

Offset: 1

Antti Karttunen, Jan 11 2023

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

Cf. A244042, A300821, A359602.

Cf. A056911 (positions of odd terms), A323239 (parity of terms), A337945.

A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);
memoA359601 = Map();
A359601(n) = if(1==n,1,my(v); if(mapisdefined(memoA359601,n,&v), v, v = -sumdiv(n,d,if(dA244042(n/d)*A359601(d),0)); mapput(memoA359601,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA244042(n/d) * a(d).

a(n) = A359602(n) - A244042(n).

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A300822 Möbius transform of A300222.

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A300823 Difference between A244042 and its Möbius transform.

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A359601 Dirichlet inverse of A244042, where A244042(n) replaces 2's with 0's in the ternary representation of n.

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