A305793 Restricted growth sequence transform of A305792, a filter sequence constructed from binary expansions of the proper divisors of n.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 15, 10, 18, 2, 19, 2, 20, 21, 7, 22, 23, 2, 15, 21, 24, 2, 25, 2, 26, 27, 28, 2, 29, 30, 31, 10, 26, 2, 32, 33, 34, 21, 28, 2, 35, 2, 36, 37, 38, 33, 39, 2, 13, 40, 41, 2, 42, 2, 43, 44, 26, 45, 46, 2, 47, 48, 43, 2, 49, 50, 51, 40, 52, 2, 53, 45, 54, 55, 56, 33, 57, 2, 58, 59

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to binary expansion of n

Formula

For all i, j:

a(i) = a(j) => A000005(i) = A000005(j).

a(i) = a(j) => A292257(i) = A292257(j).

a(i) = a(j) => A305426(i) = A305426(j).

a(i) = a(j) => A305435(i) = A305435(j).

Prog

(PARI)
\\ Needs also code from A286622:
up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
A305792(n) = { my(m=1); fordiv(n, d, if(d<n, m *= prime(A286622(d)-1))); (m); };
v305793 = rgs_transform(vector(up_to, n, A305792(n)));
A305793(n) = v305793[n];

Crossrefs

Cf. A278222, A286622, A305792, A305795.

Cf. also A293215, A300833, A304103, A305813.

Sequence in context: A328767 A319682 A329353 * A300245 A346488 A300231

Adjacent sequences: A305790 A305791 A305792 * A305794 A305795 A305796

Keyword

nonn

Author

Antti Karttunen, Jun 11 2018

Status

approved