A300823 -id:A300823 - cp's OEIS frontend

A300825 Filter sequence combining A300823(n) and A300824(n).

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 9, 2, 11, 2, 12, 13, 14, 2, 15, 16, 17, 18, 19, 2, 20, 2, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 2, 30, 31, 32, 2, 33, 34, 35, 36, 37, 2, 38, 39, 40, 41, 42, 2, 43, 2, 44, 45, 44, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 55, 56, 2, 57, 58, 59, 2, 60, 61, 62, 63, 64, 2, 65, 66, 64, 67, 68, 69

Offset: 1

Antti Karttunen, Mar 14 2018

nonn

Restricted growth sequence transform of ordered pair [A300823(n), A300824(n)].

For all i, j: a(i) = a(j) => A051953(i) = A051953(j).

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

Cf. A051953, A244042, A300222, A300823, A300824.

Cf. also A293226, A300833.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);
A300823(n) = -sumdiv(n,d,(dA244042(d));
A300222(n) = (n - A244042(n));
A300824(n) = -sumdiv(n,d,(dA300222(d));
Aux300825(n) = [A300823(n), A300824(n)];
write_to_bfile(1,rgs_transform(vector(up_to,n,Aux300825(n))),"b300825.txt");

A300824 Difference between A300222(n) and its Möbius transform.

Original entry on oeis.org

0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 4, 0, 8, 2, 8, 0, 6, 0, -2, 6, 4, 0, 8, 2, 2, 0, 0, 0, 8, 0, 6, 2, 10, 8, 12, 0, 20, 0, 28, 0, 18, 0, 16, 6, 22, 0, 22, 6, 22, 8, 24, 0, 18, 4, 8, 18, 4, 0, 16, 0, 2, 18, 2, 2, 26, 0, 4, 20, 0, 0, 24, 0, 2, 28, 0, 8, 30, 0, -2, 0, 4, 0, 0, 10, 8, 2, 16, 0, 24, 6, 16, 0, 22, 20, 14, 0, 14, 6, 40, 0, 26, 0, 32, 24

Offset: 1

Antti Karttunen, Mar 14 2018

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

Cf. A008683, A051953, A300222, A300822, A300823, A300825.

f[n_] := FromDigits[IntegerDigits[n, 3] /. 1 -> 0, 3]; Table[f@ n - DivisorSum[n, MoebiusMu[n/#] f@ # &], {n, 105}] (* Michael De Vlieger, Mar 17 2018 *)

A300222(n) = fromdigits(apply(x->(if (1==x, 0, x)), digits(n, 3)), 3);
A300824(n) = -sumdiv(n,d,(dA300222(d));

a(n) = A300222(n) - A300822(n).
a(n) = -Sum_{d|n, dA008683(n/d)*A300222(d) = Sum_{d|n, dA300822(d).
a(n) = A051953(n) - A300823(n).

A300821 Möbius transform of A244042.

Original entry on oeis.org

1, -1, 2, 4, 2, -2, 0, -4, 6, 8, 8, 8, 12, 12, 4, 10, 8, -6, 0, -14, 0, -4, 2, -8, -2, -12, 18, 12, 26, 16, 30, 20, 16, 20, 24, 24, 36, 36, 24, 44, 38, 24, 36, 28, 12, 26, 26, 20, 30, 22, 16, 24, 26, -18, -10, -24, 0, -22, 2, -28, 0, -30, 0, -20, -6, -8, 12, -20, 4, -36, 8, -24, 0, -36, -4, -36, -6, -24, 0, -50, 54, 44, 80, 24

Offset: 1

Antti Karttunen, Mar 14 2018

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

Cf. A000010, A244042, A300822, A300823.

Table[DivisorSum[n, MoebiusMu[n/#] FromDigits[IntegerDigits[#, 3] /. 2 -> 0, 3] &], {n, 84}] (* Michael De Vlieger, Mar 17 2018 *)

A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);
A300821(n) = sumdiv(n,d,moebius(n/d)*A244042(d));

a(n) = Sum_{d|n} moebius(n/d)*A244042(d).
a(n) = A000010(n) - A300822(n).
a(n) = A244042(n) - A300823(n).

cp's OEIS Frontend

A300825 Filter sequence combining A300823(n) and A300824(n).

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A300824 Difference between A300222(n) and its Möbius transform.

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A300821 Möbius transform of A244042.

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