A302787 a(1) = 0; for n > 1, a(n) = A000265(A052331(n)).

0, 1, 1, 1, 1, 3, 1, 5, 1, 9, 1, 3, 1, 17, 5, 1, 1, 33, 1, 3, 9, 65, 1, 7, 1, 129, 17, 5, 1, 11, 1, 257, 33, 513, 3, 9, 1, 1025, 65, 13, 1, 19, 1, 17, 5, 2049, 1, 129, 1, 4097, 257, 33, 1, 35, 9, 21, 513, 8193, 1, 7, 1, 16385, 3, 65, 17, 67, 1, 129, 1025, 25, 1, 37, 1, 32769, 2049, 257, 5, 131, 1, 33, 1, 65537, 1, 11, 65, 131073, 4097, 69, 1, 41, 9

Offset: 1

Author

Antti Karttunen, Apr 13 2018

Keywords

• nonn

Comments

After n=1, differs from A240535 (which gives the same terms, but with mirrored binary expansion) for the first time at n=30, where a(30) = 11, while A240535(30) = 13. Note how 11 = "1011" and 13 = "1101" in binary.

For all i, j: a(i) = a(j) => A302791(i) = A302791(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A000265, A050376, A052331, A240535, A302786, A302788, A302789, A302790, A302791.

Cf. also A246277.

Programs

PARI

up_to = 8192;
v050376 = vector(up_to);
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); };
A000265(n) = (n/2^valuation(n, 2));
A302787(n) = if(1==n,0,A000265(A052331(n)));

Formula

a(1) = 0; for n > 1, a(n) = A000265(A052331(n)).

For n > 1, a(n) = A030101(A240535(n)).

For n >= 1, A069010(a(n)) = A302790(n).