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

1,2

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

Prog

(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];

Crossrefs

Cf. A007949, A046523, A286463, A305900.

Cf. also A305891.

Sequence in context: A191248 A323156 A075994 * A325980 A366122 A182718

Adjacent sequences: A305890 A305891 A305892 * A305894 A305895 A305896

Keyword

nonn

Author

Antti Karttunen, Jun 14 2018

Status

approved