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A305789
Filter-sequence combining prime signature of n (A046523) and similar signature for GF(2)[X]-factorization (A278233).
6
1, 2, 2, 3, 4, 5, 2, 6, 7, 8, 2, 9, 2, 5, 10, 11, 12, 13, 2, 14, 15, 5, 16, 17, 18, 5, 19, 9, 16, 20, 2, 21, 5, 22, 5, 23, 2, 5, 8, 24, 2, 25, 16, 9, 26, 27, 2, 28, 7, 29, 30, 9, 16, 31, 32, 17, 8, 27, 2, 33, 2, 5, 9, 34, 35, 36, 2, 37, 15, 36, 16, 38, 2, 5, 26, 9, 5, 39, 16, 40, 41, 5, 42, 43, 44, 27, 32, 17, 16, 45, 32, 46, 5, 5, 8, 47, 2, 13, 9, 48, 42
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of ordered pair [A046523(n), A278233(n)].
For all i, j: a(i) = a(j) => A305802(i) = A305802(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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278233(n) = { my(p=0, f=vecsort((factor(Pol(binary(n))*Mod(1, 2))[, 2]), , 4)); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
Aux305789(n) = [A046523(n), A278233(n)];
v305789 = rgs_transform(vector(up_to, n, Aux305789(n)));
A305789(n) = v305789[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 10 2018
STATUS
approved