A300233 Filter sequence combining A051953(n) and A009194(n), cototient of n and gcd(n,sigma(n)).

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

Offset

1,2

Comments

Restricted growth sequence transform of P(A051953(n), A009194(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

Links

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

Example

a(20) = a(22) (= 13) because A051953(20) = A051953(22) = 12 and A009194(20) = A009194(22) = 2.

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])); }
A009194(n) = gcd(n, sigma(n));
A051953(n) = (n - eulerphi(n));
Aux300233(n) = (1/2)*(2 + ((A051953(n)+A009194(n))^2) - A051953(n) - 3*A009194(n));
write_to_bfile(1, rgs_transform(vector(65537, n, Aux300233(n))), "b300233.txt");

Crossrefs

Cf. A009194, A051953.

Cf. also A295885, A300223, A300226, A300229, A300230, A300231, A300232, A300235.

Sequence in context: A355000 A300232 A351235 * A353523 A293217 A329351

Adjacent sequences: A300230 A300231 A300232 * A300234 A300235 A300236

Keyword

nonn

Author

Antti Karttunen, Mar 01 2018

Status

approved