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

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].
• Index entries for sequences related to sigma(n).

Crossrefs

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

Cf. also A379120.

Programs

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))));

Formula

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