A293232 Restricted growth sequence transform of A293231, where A293231(n) = Product_{d|n, d<n} A019565(A193231(d)).

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, 18, 19, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 7, 35, 36, 37, 2, 38, 39, 40, 41, 42, 2, 43, 2, 44, 45, 46, 23, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 55, 56, 2, 57, 58, 59, 2, 60, 61, 62, 63, 64, 2, 65, 66, 67, 68, 69, 70, 71, 2, 72

Offset

1,2

Links

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

Prog

(PARI)
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; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler
A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) }; \\ This function from Franklin T. Adams-Watters
A293231(n) = { my(m=1); fordiv(n, d, if(d < n, m *= A019565(A193231(d)))); m; };
write_to_bfile(1, rgs_transform(vector(65537, n, A293231(n))), "b293232.txt");

Crossrefs

Cf. A019565, A193231.

Cf. A290090.

Differs from related A293215 for the first time at n=55, where a(55) = 39, while A293215(55) = 28.

Sequence in context: A351030 A329381 A293215 * A300835 A369051 A369046

Adjacent sequences: A293229 A293230 A293231 * A293233 A293234 A293235

Keyword

nonn

Author

Antti Karttunen, Oct 03 2017

Status

approved