A300241 Filter sequence combining A001065(n) and A009195(n), the sum of proper divisors of n and gcd(n,phi(n)).

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, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 40, 41, 42, 43, 2, 44, 2, 45, 46, 47, 48, 49, 2, 50, 51, 52, 2, 53, 2, 54, 55, 56, 48, 57, 2, 58, 59, 60, 2, 61, 62, 63, 64, 65, 2, 66, 37, 67, 68, 69, 70, 71, 2, 72, 73

Offset: 1

Author

Antti Karttunen, Mar 02 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of P(A001065(n), A009195(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

Examples

			a(65) = a(77) (= 48) because A001065(65) = A001065(77) = 19 and A009195(65) = A009195(77) = 1.
		

Links

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

Crossrefs

Cf. A001065, A009195.

Cf. also A300231, A300240, A300242, A300243.

Programs

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])); }
A001065(n) = (sigma(n)-n);
A009195(n) = gcd(n, eulerphi(n));
Aux300241(n) = (1/2)*(2 + ((A001065(n)+A009195(n))^2) - A001065(n) - 3*A009195(n));
write_to_bfile(1,rgs_transform(vector(65537,n,Aux300241(n))),"b300241.txt");