A300225 Filter sequence combining A296078(n) and A296091(n), the prime signatures of phi(n)+1 and sigma(n)-1, with a(1) = 1.

1, 2, 2, 3, 2, 2, 2, 3, 4, 2, 2, 5, 2, 2, 6, 7, 2, 3, 2, 6, 2, 3, 2, 6, 8, 2, 3, 3, 2, 6, 2, 3, 9, 2, 6, 10, 2, 2, 11, 2, 2, 3, 2, 9, 11, 2, 2, 3, 12, 13, 9, 6, 2, 3, 2, 11, 2, 2, 2, 2, 2, 3, 2, 14, 6, 15, 2, 16, 17, 11, 2, 11, 2, 2, 3, 2, 3, 6, 2, 15, 18, 5, 2, 6, 9, 2, 15, 2, 2, 6, 3, 19, 2, 3, 3, 9, 2, 20, 3, 21, 2, 15, 2, 11, 6

Offset: 1

Author

Antti Karttunen, Mar 01 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of P(A296078(n), A296091(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

Crossrefs

Cf. A000010, A000203, A296078, A296091.

Cf. also A296085, A300223, A300224.

Programs

PARI

up_to = 65537;
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]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A296078(n) = A046523(1+eulerphi(n));
A296091(n) = if(1==n,n,A046523(sigma(n)-1);)
Aux300225(n) = (1/2)*(2 + ((A296078(n)+A296091(n))^2) - A296078(n) - 3*A296091(n));
write_to_bfile(1,rgs_transform(vector(up_to,n,Aux300225(n))),"b300225.txt");