A305813 Restricted growth sequence transform of A305812, a filter sequence constructed from the GF(2)[X]-factorization signatures of the proper divisors of n.

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

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: A304103 A305983 A370816 * A319355 A129294 A363719

Adjacent sequences: A305810 A305811 A305812 * A305814 A305815 A305816

Keyword

nonn

Author

Antti Karttunen, Jun 11 2018

Status

approved