A319347 Filter sequence combining A000035(n) (parity of n), A003557(n), and A046523(n) (prime signature of n).

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

Offset: 1

Author

Antti Karttunen, Sep 24 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of triple [A000035(n), A003557(n), A046523(n)], or equally, of triple [A007814(n), A003557(n), A046523(n)], or equally, of ordered pair [A000035(n), A291757(n)].

For all i, j: A305801(i) = A305801(j) => a(i) = a(j) => A305891(i) = A305891(j).

Links

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

Crossrefs

Cf. A000035, A003557, A007814, A046523, A291757, A305801, A305891.

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; };
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p=0); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
v319347 = rgs_transform(vector(up_to,n,[A003557(n),(n%2),A046523(n)]));
A319347(n) = v319347[n];