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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.
7
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
1,2
LINKS
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).
PROG
(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];
CROSSREFS
Cf. A206719, A206074 (gives the positions of 2's), A257000.
Sequence in context: A300247 A318887 A305975 * A117658 A371446 A325564
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 08 2018
STATUS
approved