A322990 a(n) = A289272(floor(A289271(n)/2)).

1, 1, 2, 3, 4, 2, 5, 7, 8, 3, 9, 6, 11, 4, 10, 13, 16, 5, 17, 12, 14, 7, 19, 18, 23, 8, 25, 15, 27, 6, 29, 31, 22, 9, 20, 21, 32, 11, 26, 28, 37, 10, 41, 24, 36, 13, 43, 34, 47, 16, 38, 33, 49, 17, 44, 35, 46, 19, 53, 30, 59, 23, 40, 61, 52, 14, 64, 39, 50, 12, 67, 56, 71, 25, 54, 48, 45, 18, 73, 68, 79, 27, 81, 42, 76, 29, 58, 63, 83, 15, 55, 51, 62, 31, 92

Offset

1,3

Comments

For all n > 1, in the binary tree illustrated in A289272, the node which contains (has value) n, its parent node has value a(n).

Each n occurs exactly twice in this sequence.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A289272(floor(A289271(n)/2)).

Prog

(PARI)
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.
A289272(n) = { my(m=1, pp=1); while(n>0, pp++; while(!isprimepower(pp)||(gcd(pp, m)>1), pp++); if(n%2, m *= pp); n >>=1); (m); };
A322990(n) = A289272(A289271(n)>>1);

Crossrefs

Cf. A289271, A289272, A322988, A322991, A322992.

Cf. also A252463, A300840.

Sequence in context: A333235 A295887 A293450 * A120636 A209747 A117744

Adjacent sequences: A322987 A322988 A322989 * A322991 A322992 A322993

Keyword

nonn

Author

Antti Karttunen, Jan 01 2019

Status

approved