A322995 a(1) = 0; for n > 1, a(n) = A000265(A289271(n)).

0, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 9, 5, 1, 1, 17, 1, 3, 9, 33, 1, 17, 1, 65, 1, 5, 1, 7, 1, 1, 33, 129, 3, 9, 1, 257, 65, 5, 1, 11, 1, 17, 9, 513, 1, 129, 1, 1025, 257, 33, 1, 2049, 17, 3, 513, 4097, 1, 7, 1, 8193, 5, 1, 33, 19, 1, 65, 1025, 13, 1, 3, 1, 16385, 2049, 129, 9, 35, 1, 65, 1, 32769, 1, 11, 129, 65537, 4097, 5, 1, 21, 17, 257

Offset: 1

Author

Antti Karttunen, Jan 02 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A001221, A000265, A289271.

Cf. also A322993.

Programs

PARI

A000265(n) = (n/2^valuation(n, 2));
A289271(n) = { my(v=0,i=0,x=1); for(d=2,oo,if(n==1, return(v)); if(1==gcd(x,d)&&1==omega(d), if(!(n%d)&&1==gcd(d,n/d), v += 2^i; n /= d; x *= d); i++)); }; \\ After Rémy Sigrist's program for A289271.
A322995(n) = if(1==n,0,A000265(A289271(n)));

Formula

a(1) = 0; for n > 1, a(n) = A000265(A289271(n)).

For all n >= 1, A000120(a(n)) = A001221(n).