A090331 - OEIS

%I #19 Feb 16 2025 08:32:51

%S 1,1,2,1,3,1,4,1,5,1,6,1,7,3,8,1,9,1,10,1,11,1,12,1,13,3,14,1,15,1,16,

%T 1,17,1,18,1,19,1,20,1,21,1,22,5,23,1,24,1,25,3,26,1,27,1,28,3,29,1,

%U 30,1,31,7,32,1,33,1,34,1,35,1,36,1,37,1,38,1,39,1,40,1,41,1,42,5,43

%N Largest proper divisor of n that is also a prefix of n in binary.

%C a(n) = 1 iff A090330(n) = 0;

%C a(A090332(n))=1; a(A090334(n))>1.

%H Antti Karttunen, <a href="/A090331/b090331.txt">Table of n, a(n) for n = 2..65537</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ProperDivisor.html">Proper Divisor</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%o (PARI) A090331(n) = { my(w=binary(n),x); fordiv(n,d,if(d>1, x=binary(n/d); if(w[1..#x] == x, return(n/d)))); }; \\ _Antti Karttunen_, Jan 24 2025

%Y Cf. A032742, A007088, A090330, A090332 (after its initial 1, gives the positions of 1's), A090334 (positions of terms > 1).

%K nonn,base

%O 2,3

%A _Reinhard Zumkeller_, Nov 26 2003, corrected May 08 2004

%E Edited by _N. J. A. Sloane_, Aug 19 2008 at the suggestion of _Leroy Quet_