A300242 Filter sequence combining gcd(n,sigma(n)) and gcd(n,phi(n)), (A009194 and A009195).

1, 1, 1, 2, 1, 3, 1, 4, 5, 6, 1, 7, 1, 6, 8, 9, 1, 10, 1, 11, 5, 6, 1, 12, 13, 6, 14, 15, 1, 3, 1, 16, 8, 6, 1, 17, 1, 6, 5, 18, 1, 19, 1, 7, 20, 6, 1, 21, 22, 23, 8, 11, 1, 24, 13, 25, 5, 6, 1, 26, 1, 6, 14, 27, 1, 3, 1, 11, 8, 6, 1, 28, 1, 6, 13, 7, 1, 19, 1, 29, 30, 6, 1, 31, 1, 6, 8, 32, 1, 33, 34, 7, 5, 6, 35, 36, 1, 37, 20, 38, 1, 3, 1, 39, 20

Offset

1,4

Comments

Restricted growth sequence transform of P(A009194(n), A009195(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(15) = a(33) (= 8) because A009194(15) = A009194(33) = 3 and A009195(15) = A009195(33) = 1.
a(20) = a(52) (= 11) because A009194(20) = A009194(52) = 2 and A009195(20) = A009195(52) = 4.

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));
A009195(n) = gcd(n, eulerphi(n));
Aux300242(n) = (1/2)*(2 + ((A009194(n)+A009195(n))^2) - A009194(n) - 3*A009195(n));
write_to_bfile(1, rgs_transform(vector(65537, n, Aux300242(n))), "b300242.txt");

Crossrefs

Cf. A009194, A009195.

Cf. also A286591, A300225, A300240, A300241, A300243.

Sequence in context: A299774 A362254 A341866 * A293892 A295885 A329035

Adjacent sequences: A300239 A300240 A300241 * A300243 A300244 A300245

Keyword

nonn

Author

Antti Karttunen, Mar 02 2018

Status

approved