A379113 a(1) = 1; for n > 1, a(n) is the greatest proper unitary divisor d of n such that A048720(A065621(sigma(d)),sigma(n/d)) is equal to sigma(n).

1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 7, 3, 1, 1, 1, 1, 5, 7, 11, 1, 3, 1, 2, 1, 7, 1, 15, 1, 1, 3, 1, 7, 1, 1, 1, 3, 5, 1, 21, 1, 11, 1, 23, 1, 3, 1, 2, 3, 13, 1, 1, 11, 7, 3, 2, 1, 15, 1, 31, 7, 1, 5, 33, 1, 1, 3, 35, 1, 9, 1, 1, 3, 19, 7, 6, 1, 5, 1, 1, 1, 21, 1, 43, 3, 11, 1, 1, 7, 23, 31, 47, 1, 3, 1, 1, 1, 4, 1

Offset

1,6

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/A379119(n).

Prog

(PARI)
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1, n+n-1);
A379113(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(n/d))));

Crossrefs

Cf. A000203, A048720, A065621, A379114 (positions of terms > 1), A379119.

Cf. also A325567.

Sequence in context: A340084 A317939 A086767 * A119288 A226040 A302034

Adjacent sequences: A379110 A379111 A379112 * A379114 A379115 A379116

Keyword

nonn,new

Author

Antti Karttunen, Dec 17 2024

Status

approved