A379120 a(1) = 1; and for n > 1, a(n) is the smallest divisor d > 1 of n such that A048720(A065621(n/d),d) is equal to n.

1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 15, 2, 17, 3, 19, 5, 7, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 2, 3, 17, 7, 3, 37, 19, 39, 5, 41, 7, 43, 11, 15, 23, 47, 3, 7, 25, 51, 13, 53, 27, 55, 7, 57, 29, 59, 15, 61, 31, 63, 2, 5, 3, 67, 17, 69, 7, 71, 3, 73, 37, 15, 19, 77, 39, 79, 5, 81, 41, 83, 7, 85, 43, 87, 11, 89

Offset: 1

Author

Antti Karttunen, Dec 17 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences defined by congruent products between domains N and GF(2)[X].
• Index entries for sequences related to polynomials in ring GF(2)[X].

Crossrefs

Cf. A048720, A065621, A115872, A325565, A325566, A325567.

Cf. also A379119.

Programs

PARI

A048720(b,c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1,n+n-1);
A379120(n) = if(1==n,n,fordiv(n,d,if((d>1)&&A048720(A065621(n/d),d)==n,return(d))));

Formula

a(n) = n / A325567(n).