A378226 -id:A378226 - cp's OEIS frontend

A378230 Positions of 0's in A378226, where A278226 is XOR-Moebius transform of A318457, and A318457(n) = n XOR (sigma(n)-n).

6, 14, 28, 42, 50, 62, 72, 114, 124, 150, 186, 248, 254, 376, 402, 412, 426, 434, 474, 496, 498, 508, 762, 784, 786, 796, 868, 938, 978, 994, 1002, 1016, 1302, 1528, 1568, 1578, 1626, 1778, 1834, 1852, 1888, 1948, 1988, 2032, 3056, 3064, 3094, 3282, 3350, 3556, 3568, 3644, 3682, 3794, 3858, 3868, 3882, 3954, 4064

Offset: 1

Antti Karttunen, Nov 26 2024

nonn

Positions of 0's in A378226.
Cf. A001065, A318457.
Subsequences: A000396 (at least the even terms).

A318457(n) = bitxor(n,sigma(n)-n);
A378226(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A318457(d)))); (v); }
isA378230(n) = (0==A378226(n));

A378441 Fixed points of A378226, where A278226 is XOR-Moebius transform of A318457, and A318457(n) = n XOR (sigma(n)-n).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 11, 13, 16, 17, 19, 23, 27, 29, 31, 32, 37, 41, 43, 47, 53, 59, 61, 64, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251, 256, 257, 263, 269, 271, 277, 281

Offset: 1

Antti Karttunen, Nov 26 2024

nonn

Cf. A000040 (subsequence), A001065, A003987, A318457, A378226.

A318457(n) = bitxor(n,sigma(n)-n);
A378226(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A318457(d)))); (v); }
isA378441(n) = (A378226(n)==n);

{k such that A378226(k) is equal to k}.

A378227 XOR-Moebius transform of A318467, where A318467(n) = 2*n XOR sigma(n).

Original entry on oeis.org

3, 4, 1, 8, 15, 6, 5, 16, 29, 14, 25, 12, 23, 6, 11, 32, 51, 30, 49, 12, 13, 22, 53, 24, 33, 14, 1, 12, 39, 126, 29, 64, 105, 70, 127, 20, 111, 70, 99, 24, 123, 58, 121, 12, 15, 38, 109, 48, 93, 30, 31, 28, 95, 22, 51, 24, 17, 14, 73, 172, 71, 6, 1, 128, 205, 114, 193, 140, 221, 102, 197, 72, 219, 142, 205, 108

Offset: 1

Antti Karttunen, Nov 26 2024

nonn

Unique sequence satisfying SumXOR_{d divides n} a(d) = A318467(n) for all n > 0, where SumXOR is the analog of summation under the binary XOR operation. See A295901 for a list of some of the properties of Xor-Moebius transform.

Cf. A000203, A003987, A256739, A296203, A318467.

Cf. also A083254, A378226.

A318467(n) = bitxor(2*n, sigma(n));
A378227(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A318467(d)))); (v); }

a(n) = 2*A256739(n) XOR A296203(n).

cp's OEIS Frontend

A378230 Positions of 0's in A378226, where A278226 is XOR-Moebius transform of A318457, and A318457(n) = n XOR (sigma(n)-n).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A378441 Fixed points of A378226, where A278226 is XOR-Moebius transform of A318457, and A318457(n) = n XOR (sigma(n)-n).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A378227 XOR-Moebius transform of A318467, where A318467(n) = 2*n XOR sigma(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula