A319338 Filter sequence combining the 2-adic valuation of n (A007814) with gcd(n,sigma(n)) (A009194).

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

Offset: 1

Author

Antti Karttunen, Sep 24 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of ordered pair [A007814(n), A009194(n)].

Links

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

Crossrefs

Cf. A007814, A009194, A305801, A319346.

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; };
A007814(n) = valuation(n,2);
A009194(n) = gcd(n, sigma(n));
v319338 = rgs_transform(vector(up_to,n,[A007814(n),A009194(n)]));
A319338(n) = v319338[n];