

A305813


Restricted growth sequence transform of A305812, a filter sequence constructed from the GF(2)[X]factorization signatures of the proper divisors of n.


4



1, 2, 2, 3, 2, 4, 2, 5, 3, 5, 2, 6, 2, 4, 5, 7, 2, 8, 2, 9, 4, 4, 2, 10, 11, 4, 12, 6, 2, 10, 2, 13, 4, 14, 5, 15, 2, 4, 4, 16, 2, 17, 2, 6, 18, 12, 2, 19, 3, 20, 14, 6, 2, 21, 5, 10, 4, 12, 2, 22, 2, 4, 6, 23, 5, 24, 2, 25, 12, 26, 2, 27, 2, 4, 28, 6, 4, 29, 2, 30, 31, 4, 2, 32, 33, 12, 12, 10, 2, 34, 4, 35, 4, 4, 5, 36, 2, 8, 8, 37, 2, 38, 2, 10, 39
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OFFSET

1,2


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences operating on GF(2)[X]polynomials


FORMULA

For all i, j:
a(i) = a(j) => A000005(i) = A000005(j).
a(i) = a(j) => A294881(i) = A294881(j).
a(i) = a(j) => A294882(i) = A294882(j).


PROG

(PARI)
\\ Needs also code from A305788:
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; };
A305812(n) = if(1==n, 0, my(m=1); fordiv(n, d, if((d>1)&&(d<n), m *= prime(A305788(d)1))); (m));
v305813 = rgs_transform(vector(up_to, n, A305812(n)));
A305813(n) = v305813[n];


CROSSREFS

Cf. A278233, A305788, A305812, A305815.
Cf. also A305793.
Sequence in context: A300224 A304103 A305983 * A319355 A129294 A323914
Adjacent sequences: A305810 A305811 A305812 * A305814 A305815 A305816


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jun 11 2018


STATUS

approved



