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

Author

Reinhard Zumkeller, Nov 26 2003, corrected May 08 2004

Keywords

• nonn
• base

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

Crossrefs

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

Programs

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

Extensions

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