A379119 a(1) = 1; for n > 1, a(n) is the smallest unitary divisor d > 1 of n such that A048720(A065621(sigma(n/d)),sigma(d)) is equal to sigma(n).

1, 2, 3, 4, 5, 2, 7, 8, 9, 2, 11, 4, 13, 2, 5, 16, 17, 18, 19, 4, 3, 2, 23, 8, 25, 13, 27, 4, 29, 2, 31, 32, 11, 34, 5, 36, 37, 38, 13, 8, 41, 2, 43, 4, 45, 2, 47, 16, 49, 25, 17, 4, 53, 54, 5, 8, 19, 29, 59, 4, 61, 2, 9, 64, 13, 2, 67, 68, 23, 2, 71, 8, 73, 74, 25, 4, 11, 13, 79, 16, 81, 82, 83, 4, 85, 2, 29, 8, 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].

Index entries for sequences related to sigma(n).

Formula

a(n) = n / A379113(n).

Prog

(PARI)
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1, n+n-1);
A379119(n) = if(1==n, n, my(s=sigma(n)); fordiv(n, d, if((d>1) && 1==gcd(d, n/d) && A048720(A065621(sigma(n/d)), sigma(d))==s, return(d))));

Crossrefs

Cf. A000203, A048720, A065621, A379113, A379114 (positions of terms such that a(n) < n).

Cf. also A379120.

Sequence in context: A323130 A028233 A375400 * A216972 A066296 A162961

Adjacent sequences: A379116 A379117 A379118 * A379120 A379122 A379124

Keyword

nonn,new

Author

Antti Karttunen, Dec 17 2024

Status

approved