A325567 -id:A325567 - cp's OEIS frontend

A325573 Odd numbers n that have divisor d > 1 such that A048720(A065621(d),n/d) = n.

9, 21, 33, 35, 45, 49, 65, 75, 93, 105, 129, 133, 135, 153, 155, 161, 165, 189, 195, 217, 225, 259, 273, 279, 297, 309, 315, 341, 345, 381, 385, 403, 441, 465, 513, 525, 527, 561, 567, 585, 589, 597, 611, 621, 635, 645, 651, 681, 693, 705, 713, 729, 765, 775, 793, 819, 837, 889, 899, 945, 961, 1025, 1029, 1035, 1057, 1065

Offset: 1

Antti Karttunen, May 10 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A048720, A065621, A115872, A325566, A325567, A325571.

Subsequence of A071904 and of A325572.

A048720(b,c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1,n+n-1);
isA325573(n) = ((n%2)&&fordiv(n,d,if(A048720(A065621(n/d),d)==n,return(d

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.

Original entry on oeis.org

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

Antti Karttunen, Dec 17 2024

nonn

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

Cf. also A379119.

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))));

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

A379127 a(1) = 1; for n > 1, a(n) is the largest proper divisor d of 2n-1 such that A048720(A065621(d),(2n-1)/d) is equal to 2n-1.

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 11, 5, 1, 1, 1, 1, 3, 1, 7, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 43, 1, 19, 9, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 23, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Antti Karttunen, Dec 21 2024

nonn

The position of the first occurrence of odd numbers k = 1, 3, 5, 7, 9, ... in this sequence is given by (1/2) * (A379128(2*k-1)+1).

Odd bisection of A325567.

Cf. A048720, A065621, A277320, A379128.

A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1, n+n-1);
A325567(n) = if(1==n, n, fordiv(n, d, if((d>1)&&A048720(A065621(n/d), d)==n, return(n/d))));
A379127(n) = A325567(2*n-1);

a(n) = A325567(2*n-1).

cp's OEIS Frontend

A325573 Odd numbers n that have divisor d > 1 such that A048720(A065621(d),n/d) = n.

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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.

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A379127 a(1) = 1; for n > 1, a(n) is the largest proper divisor d of 2n-1 such that A048720(A065621(d),(2n-1)/d) is equal to 2n-1.

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