A304751 Filter sequence: Restricted growth sequence transform of function that gives the least natural number with the same prime signature that (0,1)-polynomial encoded in the binary expansion of n has when it is factored over Q.

1, 2, 2, 3, 2, 4, 2, 5, 4, 4, 2, 6, 2, 4, 4, 7, 2, 8, 2, 6, 4, 4, 2, 9, 2, 4, 6, 6, 2, 8, 2, 10, 4, 4, 4, 11, 2, 4, 4, 9, 2, 8, 2, 6, 8, 4, 2, 12, 4, 4, 4, 6, 2, 11, 2, 9, 4, 4, 2, 11, 2, 4, 8, 13, 4, 8, 2, 6, 2, 8, 2, 14, 2, 4, 8, 6, 2, 8, 2, 12, 2, 4, 2, 11, 4, 4, 2, 9, 2, 15, 2, 6, 4, 4, 4, 16, 2, 8, 6, 6, 2, 8, 2, 9, 8

Offset: 1

Author

Antti Karttunen, Jun 08 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A206719, A206074 (gives the positions of 2's), A257000.

Cf. also A046523 (A101296), A278233, A284010, A284011.

Programs

PARI

up_to = 65537;
rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
Aux304751(n) = { my(p=0, f=vecsort((factor(Pol(binary(n)))[, 2]), , 4)); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }
v304751 = rgs_transform(vector(up_to,n,Aux304751(n)));
A304751(n) = v304751[n];

Formula

For all i, j: a(i) = a(j) => A206719(i) = A206719(j).

For all i, j: a(i) = a(j) => A257000(i) = A257000(j).