

A286621


Restricted growth sequence computed for filtersequence A278221, related to the conjugated prime factorization (see A122111).


16



1, 2, 3, 2, 4, 5, 6, 2, 3, 7, 8, 5, 9, 10, 7, 2, 11, 5, 12, 7, 13, 14, 15, 5, 4, 16, 3, 10, 17, 18, 19, 2, 20, 21, 10, 5, 22, 23, 24, 7, 25, 26, 27, 14, 7, 28, 29, 5, 6, 7, 30, 16, 31, 5, 20, 10, 32, 33, 34, 18, 35, 36, 13, 2, 37, 38, 39, 21, 40, 26, 41, 5, 42, 43, 7, 23, 14, 44, 45, 7, 3, 46, 47, 26, 48, 49, 50, 14, 51, 18, 24, 28, 52, 53, 54, 5, 55, 10, 20, 7
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OFFSET

1,2


COMMENTS

When filtering sequences (by equivalence class partitioning), this sequence (with its modestly sized terms) can be used instead of A278221 (which has some huge terms), because for all i, j it holds that: a(i) = a(j) <=> A278221(i) = A278221(j).
For example, for all i, j: a(i) = a(j) => A006530(i) = A006530(j).


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000


FORMULA

Construction: we start with a(1)=1 for A278221(1)=1, and then after, for all n > 1, we use the least so far unused natural number k for a(n) if A278221(n) has not been encountered before, otherwise [whenever A278221(n) = A278221(m), for some m < n], we set a(n) = a(m).


EXAMPLE

For n=2, A278221(2) = 2, which has not been encountered before, thus we allot for a(2) the least so far unused number, which is 2, thus a(2) = 2.
For n=3, A278221(3) = 4, which has not been encountered before, thus we allot for a(3) the least so far unused number, which is 3, thus a(3) = 3.
For n=4, A278221(4) = 2, which was already encountered as A278221(2), thus we set a(4) = a(2) = 2.
For n=9, A278221(9) = 4, which was already encountered at n=3, thus a(9) = 3.
For n=13, A278221(13) = 64, which has not been encountered before, thus we allot for a(13) the least so far unused number, which is 9, thus a(13) = 9.
For n=194, A278221(194) = 50331648, which has not been encountered before, thus we allot for a(194) the least so far unused number, which is 106, thus a(194) = 106.
For n=388, A278221(388) = 50331648, which was already encountered at n=194, thus a(388) = a(194) = 106.


PROG

(PARI)
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; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)1, " ", vec[n])); }
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]1)); factorback(f)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from Charles R Greathouse IV, Aug 17 2011
A278221(n) = A046523(A122111(n));
write_to_bfile(1, rgs_transform(vector(10000, n, A278221(n))), "b286621.txt");


CROSSREFS

Cf. A278221, A006530, A122111.
Cf. also A101296, A286603, A286605, A286610, A286619, A286622, A286626, A286378 for similarly constructed sequences.
Sequence in context: A120641 A008666 A240854 * A295876 A322590 A325381
Adjacent sequences: A286618 A286619 A286620 * A286622 A286623 A286624


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 11 2017


STATUS

approved



