A302791 A filter sequence for Fermi-Dirac factorization: restricted growth sequence transform of A046523(A302024(n)).

1, 2, 2, 2, 2, 3, 2, 4, 2, 4, 2, 3, 2, 4, 4, 2, 2, 4, 2, 3, 4, 4, 2, 5, 2, 4, 4, 4, 2, 6, 2, 4, 4, 4, 3, 4, 2, 4, 4, 6, 2, 6, 2, 4, 4, 4, 2, 4, 2, 4, 4, 4, 2, 6, 4, 7, 4, 4, 2, 5, 2, 4, 3, 4, 4, 6, 2, 4, 4, 6, 2, 7, 2, 4, 4, 4, 4, 6, 2, 4, 2, 4, 2, 6, 4, 4, 4, 7, 2, 7, 4, 4, 4, 4, 4, 6, 2, 4, 3, 4, 2, 6, 2, 7, 6

Offset

1,2

Comments

For all i, j: a(i) = a(j) => A064547(i) = A064547(j).

For all i, j: a(i) = a(j) => A302790(i) = A302790(j).

See also comments in A302024.

Links

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

Prog

(PARI)
allocatemem(2^30);
up_to = 65537;
v050376 = vector(up_to);
A050376(n) = v050376[n];
ispow2(n) = (n && !bitand(n, n-1));
i = 0; for(n=1, oo, if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to, break));
A052331(n) = { my(s=0, e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler
A302024(n) = A005940(1+A052331(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux302791(n) = A046523(A302024(n));
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])); }
write_to_bfile(1, rgs_transform(vector(up_to, n, Aux302791(n))), "b302791.txt");

Crossrefs

Cf. A037445, A046523, A050376 (gives the positions of 2's), A052331, A064547, A293442, A302024, A302787, A302790.

Sequence in context: A178930 A126759 A293444 * A373988 A334868 A305979

Adjacent sequences: A302788 A302789 A302790 * A302792 A302793 A302794

Keyword

nonn

Author

Antti Karttunen, Apr 15 2018

Status

approved