A296085 Filter sequence combining A296078(n) and A296092(n), the prime signatures of 1+phi(n) and 1+sigma(n).

1, 2, 1, 3, 1, 1, 2, 4, 5, 1, 1, 1, 5, 2, 6, 7, 1, 8, 5, 9, 5, 1, 2, 9, 10, 1, 1, 5, 1, 9, 5, 11, 12, 5, 6, 13, 5, 1, 14, 5, 1, 1, 13, 15, 9, 1, 2, 3, 5, 15, 16, 17, 5, 2, 1, 6, 4, 5, 1, 2, 13, 1, 18, 19, 14, 15, 5, 16, 20, 14, 1, 21, 13, 5, 3, 5, 1, 6, 4, 15, 15, 1, 5, 21, 16, 5, 12, 1, 5, 14, 1, 22, 5, 5, 2, 15, 13, 13, 1, 5, 1, 15, 18, 9, 9

Offset: 1

Author

Antti Karttunen, Dec 08 2017

Keywords

• nonn

Comments

Restricted growth sequence transform of P(A296078(n), A296092(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

For all i, j:

a(i) = a(j) => A296213(i) = A296213(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Eric Weisstein's World of Mathematics, Pairing Function
• Wikipedia, Pairing Function

Crossrefs

Cf. A000010, A000203, A046523, A296078, A296092, A296213.

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));
A296092(n) = A046523(1+sigma(n));
Anotsubmitted5(n) = (1/2)*(2 + ((A296078(n)+A296092(n))^2) - A296078(n) - 3*A296092(n));
write_to_bfile(1,rgs_transform(vector(up_to,n,Anotsubmitted5(n))),"b296085.txt");