A090331 Largest proper divisor of n that is also a prefix of n in binary.

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, 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, 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

Offset

2,3

Comments

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

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

Links

Antti Karttunen, Table of n, a(n) for n = 2..65537

Eric Weisstein's World of Mathematics, Proper Divisor

Index entries for sequences related to binary expansion of n

Prog

(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

Crossrefs

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

Sequence in context: A342703 A249068 A308073 * A338759 A229994 A165818

Adjacent sequences: A090328 A090329 A090330 * A090332 A090333 A090334

Keyword

nonn,base

Author

Reinhard Zumkeller, Nov 26 2003, corrected May 08 2004

Extensions

Edited by N. J. A. Sloane, Aug 19 2008 at the suggestion of Leroy Quet

Status

approved