A305893 Filter sequence combining 3-adic valuation (A007949) and the prime signature (A046523) of n.

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

Offset: 1

Author

Antti Karttunen, Jun 14 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A286463, of the ordered pair [A007949(n), A046523(n)].

Links

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

Crossrefs

Cf. A007949, A046523, A286463, A305900.

Cf. also 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; };
A007949(n) = valuation(n,3);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux305893(n) = [A007949(n), A046523(n)];
v305893 = rgs_transform(vector(up_to,n,Aux305893(n)));
A305893(n) = v305893[n];