A324648 -id:A324648 - cp's OEIS frontend

A324649 Numbers k such that A318458(k) (bitwise-AND of k and sigma(k)-k) is equal to k.

6, 20, 28, 36, 66, 72, 88, 100, 104, 114, 132, 150, 240, 258, 264, 272, 280, 304, 354, 368, 392, 402, 464, 496, 498, 516, 550, 552, 642, 644, 680, 708, 748, 770, 774, 784, 786, 834, 836, 840, 860, 978, 1026, 1032, 1040, 1044, 1056, 1062, 1064, 1068, 1074, 1092, 1104, 1120, 1184, 1232, 1266, 1312, 1362, 1376, 1410, 1504

Offset: 1

Antti Karttunen, Mar 14 2019

nonn

Positions of zeros in A324648. Fixed points of A318458, also positions of the records in the latter.
Intersection with A324652 gives A324643.
The odd terms are: 7425, 76545, 92565, ... (A324897).

Cf. A318458, A324648, A324652.

Cf. A000396, A324643, A324897, A324898 (subsequences).

Select[Range@ 1600, BitAnd[#, DivisorSigma[1, #] - #] == # &] (* Michael De Vlieger, Apr 21 2019, after Vincenzo Librandi at A318458 *)

for(n=1,oo,if(bitand(n,sigma(n)-n)==n, print1(n, ", ")));

A324658 a(n) = n - A324659(n), where A324659(n) is half of bitwise-AND of 2*n and sigma(n).

Original entry on oeis.org

1, 2, 1, 4, 4, 0, 3, 8, 9, 2, 9, 0, 8, 2, 3, 16, 16, 0, 17, 0, 5, 4, 19, 0, 16, 10, 11, 0, 16, 26, 15, 32, 33, 32, 35, 0, 36, 32, 35, 0, 40, 10, 41, 4, 8, 10, 39, 0, 33, 16, 19, 4, 36, 2, 19, 0, 17, 18, 33, 40, 32, 14, 11, 64, 65, 2, 65, 64, 69, 6, 67, 8, 72, 66, 65, 8, 77, 10, 71, 0, 65, 64, 81, 4, 65, 20, 67, 0, 80

Offset: 1

Antti Karttunen, Mar 14 2019

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to binary expansion of n
Index entries for sequences related to sigma(n)

Cf. A000203, A004198, A318468, A324648, A324659.

Cf. A324652 (positions of zeros).

Array[# - BitAnd[2*#, DivisorSigma[1, #]]/2 &, 100] (* Paolo Xausa, Mar 13 2024 *)

A324658(n) = (n-(bitand(2*n,sigma(n))/2));

a(n) = n - A324659(n) = n - A318468(n)/2 = n - ((2*n AND sigma(n))/2).

A324659 a(n) = (1/2)A318468(n), where A318468(n) is bitwise-AND of 2n and sigma(n).

Original entry on oeis.org

0, 0, 2, 0, 1, 6, 4, 0, 0, 8, 2, 12, 5, 12, 12, 0, 1, 18, 2, 20, 16, 18, 4, 24, 9, 16, 16, 28, 13, 4, 16, 0, 0, 2, 0, 36, 1, 6, 4, 40, 1, 32, 2, 40, 37, 36, 8, 48, 16, 34, 32, 48, 17, 52, 36, 56, 40, 40, 26, 20, 29, 48, 52, 0, 0, 64, 2, 4, 0, 64, 4, 64, 1, 8, 10, 68, 0, 68, 8, 80, 16, 18, 2, 80, 20, 66, 20, 88, 9, 80

Offset: 1

Antti Karttunen, Mar 14 2019

Cf. A000203, A004198, A318458, A318468, A324648, A324658.

Cf. A324652 (fixed points).

Array[BitAnd[2*#, DivisorSigma[1, #]]/2 &, 100] (* Paolo Xausa, Mar 11 2024 *)

PARI
```
A324659(n) = (bitand(2*n,sigma(n))/2);
```

a(n) = A318468(n)/2.

a(n) = n - A324658(n).

cp's OEIS Frontend

A324649 Numbers k such that A318458(k) (bitwise-AND of k and sigma(k)-k) is equal to k.

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PARI

A324658 a(n) = n - A324659(n), where A324659(n) is half of bitwise-AND of 2*n and sigma(n).

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Author

Keywords

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Programs

Mathematica

PARI

Formula

A324659 a(n) = (1/2)A318468(n), where A318468(n) is bitwise-AND of 2n and sigma(n).

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Author

Keywords

Links

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Programs

Mathematica

PARI

Formula

cp's OEIS Frontend

A324649 Numbers k such that A318458(k) (bitwise-AND of k and sigma(k)-k) is equal to k.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

A324658 a(n) = n - A324659(n), where A324659(n) is half of bitwise-AND of 2*n and sigma(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A324659 a(n) = (1/2)*A318468(n), where A318468(n) is bitwise-AND of 2*n and sigma(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A324659 a(n) = (1/2)A318468(n), where A318468(n) is bitwise-AND of 2n and sigma(n).