A300240 Filter sequence combining A009195(n) and A046523(n), i.e., gcd(n,phi(n)) and the prime signature of n.

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

Offset: 1

Author

Antti Karttunen, Mar 02 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of P(A009195(n), A046523(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

Examples

			a(6) = a(10) (= 4) because both 6 and 10 are nonsquare semiprimes, and A009195(6) = A009195(10) = 2.
		

Links

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

Crossrefs

Cf. A009195, A046523.

Cf. also A300230, A300241, 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])); }
A009195(n) = gcd(n, eulerphi(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux300240(n) = (1/2)*(2 + ((A046523(n)+A009195(n))^2) - A046523(n) - 3*A009195(n));
write_to_bfile(1,rgs_transform(vector(65537,n,Aux300240(n))),"b300240.txt");