A325641 a(1) = 1; for n > 1, a(n) = n/d for the least divisor d > 1 of n such that A048720(d,k) = n for some k.

1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 9, 1, 10, 3, 11, 1, 12, 1, 13, 9, 14, 1, 15, 1, 16, 11, 17, 5, 18, 1, 19, 13, 20, 1, 21, 1, 22, 15, 23, 1, 24, 7, 25, 17, 26, 1, 27, 1, 28, 19, 29, 1, 30, 1, 31, 21, 32, 13, 33, 1, 34, 1, 35, 1, 36, 1, 37, 25, 38, 1, 39, 1, 40, 1, 41, 1, 42, 17, 43, 1, 44, 1, 45, 1, 46, 3, 47, 19

Offset: 1

Author

Antti Karttunen, May 11 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to polynomials in ring GF(2)[X]

Crossrefs

Cf. A048720, A325642, A325643.

Cf. A325559 (positions of ones after the initial 1).

Programs

PARI

A325641(n) = if(1==n,n, my(p = Pol(binary(n))*Mod(1, 2)); fordiv(n,d,if((d>1),my(q = Pol(binary(d))*Mod(1, 2)); if(0==(p%q), return(n/d)))));

Formula

a(n) = n / A325643(n).