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

1,2

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].

Formula

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

Prog

(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))));

Crossrefs

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

Cf. also A379119.

Sequence in context: A331959 A109395 A145254 * A163457 A285708 A072593

Adjacent sequences: A379117 A379118 A379119 * A379122 A379124 A379129

Keyword

nonn,new

Author

Antti Karttunen, Dec 17 2024

Status

approved