A300245 Filter sequence combining arithmetic derivative (A003415) with its Möbius transform (A300251).

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 11, 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, 27, 39, 40, 41, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 40, 60, 61, 62, 2, 63, 36, 64, 65, 66

Offset

1,2

Comments

Restricted growth sequence transform of ordered pair [A003415(n), A300251(n)].

Links

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

Example

a(16) = a(28) (= 11) because both A003415(16) = A003415(28) = 32 and A300251(16) = A300251(28) = 20.

Prog

(PARI)
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])); }
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A300251(n) = sumdiv(n, d, moebius(n/d)*A003415(d));
Aux300245(n) = [A003415(n), A300251(n)];
write_to_bfile(1, rgs_transform(vector(65537, n, Aux300245(n))), "b300245.txt");

Crossrefs

Cf. A003415, A300249, A300251, A300252, A300253.

Sequence in context: A319682 A329353 A305793 * A346488 A374479 A300231

Adjacent sequences: A300242 A300243 A300244 * A300246 A300247 A300248

Keyword

nonn

Author

Antti Karttunen, Mar 08 2018

Status

approved