A305891 Filter sequence combining 2-adic valuation (A007814) and the prime signature (A046523) 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, 7, 5, 13, 8, 3, 14, 3, 15, 9, 5, 9, 16, 3, 5, 9, 12, 3, 14, 3, 8, 17, 5, 3, 18, 7, 11, 9, 8, 3, 19, 9, 12, 9, 5, 3, 20, 3, 5, 17, 21, 9, 14, 3, 8, 9, 14, 3, 22, 3, 5, 17, 8, 9, 14, 3, 18, 23, 5, 3, 20, 9, 5, 9, 12, 3, 24, 9, 8, 9, 5, 9, 25, 3, 11, 17, 16, 3, 14, 3, 12, 26, 5, 3, 27, 3

Offset

1,2

Comments

Restricted growth sequence transform of A286161, of the ordered pair [A007814(n), A046523(n)].

For all i, j: a(i) = a(j) => A291761(i) = A291761(j).

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; };
A007814(n) = valuation(n, 2);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux305891(n) = [A007814(n), A046523(n)];
v305891 = rgs_transform(vector(up_to, n, Aux305891(n)));
A305891(n) = v305891[n];

Crossrefs

Cf. A286161, A291761, A305801.

Cf. also A305893.

Sequence in context: A291761 A319337 A373250 * A319347 A318888 A323079

Adjacent sequences: A305888 A305889 A305890 * A305892 A305893 A305894

Keyword

nonn

Author

Antti Karttunen, Jun 14 2018

Status

approved