A300226 Filter sequence combining A046523(n) and A052126(n), the prime signature of n and n/(largest prime dividing n).

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

Offset: 1

Author

Antti Karttunen, Mar 01 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of P(A046523(n), A052126(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 are nonsquare semiprimes (2*3 and 2*5), and when the largest prime factor is divided out, both yield the same quotient, 2.
		

Links

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

Crossrefs

Cf. A046523, A052126.

Cf. also A291761, A300229.

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])); }
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A052126(n) = if(1==n,n, my(f=factor(n)[, 1], gpf = f[#f]); n/gpf); \\ After code in A052126.
Aux300226(n) = (1/2)*(2 + ((A052126(n)+A046523(n))^2) - A052126(n) - 3*A046523(n));
write_to_bfile(1,rgs_transform(vector(65537,n,Aux300226(n))),"b300226.txt");