A357111 For n >= 1, a(n) = n / A076775(n).

1, 1, 3, 1, 5, 3, 7, 1, 9, 1, 11, 3, 13, 7, 15, 1, 17, 9, 19, 1, 1, 11, 23, 3, 25, 13, 27, 7, 29, 3, 31, 1, 3, 17, 35, 9, 37, 19, 39, 1, 41, 1, 43, 11, 45, 23, 47, 3, 49, 5, 51, 13, 53, 27, 55, 7, 57, 29, 59, 3, 61, 31, 3, 1, 65, 3, 67, 17, 23, 7, 71, 9, 73, 37, 75

Offset: 1

Author

Ctibor O. Zizka, Sep 11 2022

Keywords

• nonn
• base
• look

Examples

			a(12) = 12 / A076775(12) = 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000265, A032533, A076775, A354837.

Programs

Maple

f:= proc(n) local L,i;
  L:= convert(n,base,2);
  n/igcd(n,add(10^(i-1)*L[i],i=1..nops(L)));
end proc:
map(f, [$1..100]); # Robert Israel, Sep 11 2022

Mathematica

a[n_] := n / GCD[n, FromDigits@IntegerDigits[n, 2]]; Array[a, 100] (* Amiram Eldar, Sep 11 2022 *)

Python

from math import gcd
def A357111(n): return n//gcd(n,int(bin(n)[2:])) # Chai Wah Wu, Sep 12 2022

Formula

a(n) = 1 for n = A076775(A032533(k)).

a(n) != n for n = A354837(k), a(n) = n for all other odd n.

a(n) != A000265(n) for n = 10*k and for n = 2^r * A354837(k), r >= 0, k >= 1.