A319337 Filter sequence combining gcd(n,tau(n)) (= A009191) with the prime signature of n (A046523).

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

Offset: 1

Author

Antti Karttunen, Sep 24 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of ordered pair [A009191(n), A046523(n)].

Links

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

Crossrefs

Cf. A009191, A046523, A101296, A300230, A300240, A305801, A319338.

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; };
A009191(n) = gcd(n, numdiv(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p=0); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
v319337 = rgs_transform(vector(up_to,n,[A009191(n),A046523(n)]));
A319337(n) = v319337[n];