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

Author

Antti Karttunen, Jun 11 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A278233, A305788, A305812, A305815.

Cf. also A305793.

Programs

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)&&(dA305788(d)-1))); (m));
v305813 = rgs_transform(vector(up_to, n, A305812(n)));
A305813(n) = v305813[n];

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).