A318518 -id:A318518 - cp's OEIS frontend

A318458 a(n) = n AND A001065(n), where AND is bitwise-and (A004198) & A001065 = sum of proper divisors.

0, 0, 1, 0, 1, 6, 1, 0, 0, 8, 1, 0, 1, 10, 9, 0, 1, 16, 1, 20, 1, 6, 1, 0, 0, 16, 9, 28, 1, 10, 1, 0, 1, 0, 1, 36, 1, 6, 1, 32, 1, 34, 1, 40, 33, 10, 1, 0, 0, 34, 17, 36, 1, 2, 17, 0, 17, 32, 1, 44, 1, 34, 41, 0, 1, 66, 1, 0, 1, 66, 1, 72, 1, 8, 1, 64, 1, 74, 1, 64, 0, 0, 1, 4, 21, 6, 1, 88, 1, 16, 17, 76, 1, 18, 25, 0, 1, 64, 33, 100, 1, 98, 1, 104, 65

Offset: 1

Antti Karttunen, Aug 26 2018

The peculiar look of the scatterplot is partly an artifact of the logarithmic scale. Compare also to the scatterplot of A318468.

Cf. A000203, A001065, A004198, A033879, A318456, A318457.

Cf. also A318468, A318508, A318518, A318463.

[SumOfDivisors(n)-BitwiseOr(n, SumOfDivisors(n)-n): n in [1..100]]; // Vincenzo Librandi, Aug 29 2018

Table[BitAnd[n, DivisorSigma[1, n] - n], {n, 100}] (* Vincenzo Librandi, Aug 29 2018 *)

PARI
```
A318458(n) = bitand(n,sigma(n)-n);
```

a(n) = A004198(n, A001065(n)).

a(n) = A000203(n) - A318456(n) = (A000203(n)-A318457(n))/2.

A318517 a(n) = A032742(n) XOR n-A032742(n), where XOR is bitwise-xor (A003987) and A032742 = the largest proper divisor of n.

Original entry on oeis.org

1, 0, 3, 0, 5, 0, 7, 0, 5, 0, 11, 0, 13, 0, 15, 0, 17, 0, 19, 0, 9, 0, 23, 0, 17, 0, 27, 0, 29, 0, 31, 0, 29, 0, 27, 0, 37, 0, 23, 0, 41, 0, 43, 0, 17, 0, 47, 0, 45, 0, 51, 0, 53, 0, 39, 0, 53, 0, 59, 0, 61, 0, 63, 0, 57, 0, 67, 0, 57, 0, 71, 0, 73, 0, 43, 0, 73, 0, 79, 0, 45, 0, 83, 0, 85, 0, 39, 0, 89, 0, 67, 0, 33, 0, 95

Offset: 1

Antti Karttunen, Aug 28 2018

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to binary expansion of n

Cf. A003987, A032742, A060681, A106409, A318507, A318516, A318518.

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318517(n) = bitxor(A032742(n),n-A032742(n));

a(n) = A003987(A032742(n), A060681(n)).

a(n) = n - 2*A318518(n).

A318516 a(n) = A032742(n) OR n-A032742(n), where OR is bitwise-or (A003986) and A032742 = the largest proper divisor of n.

Original entry on oeis.org

1, 1, 3, 2, 5, 3, 7, 4, 7, 5, 11, 6, 13, 7, 15, 8, 17, 9, 19, 10, 15, 11, 23, 12, 21, 13, 27, 14, 29, 15, 31, 16, 31, 17, 31, 18, 37, 19, 31, 20, 41, 21, 43, 22, 31, 23, 47, 24, 47, 25, 51, 26, 53, 27, 47, 28, 55, 29, 59, 30, 61, 31, 63, 32, 61, 33, 67, 34, 63, 35, 71, 36, 73, 37, 59, 38, 75, 39, 79, 40, 63, 41, 83, 42

Offset: 1

Antti Karttunen, Aug 28 2018

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to binary expansion of n

Cf. A003986, A032742, A060681, A318506, A318514, A318517, A318518.

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318516(n) = bitor(A032742(n),n-A032742(n));

a(n) = A003986(A032742(n), A060681(n)).

a(n) = n - A318518(n).

A318515 a(n) = n AND A032742(n), where AND is bitwise-and (A004198) and A032742 = the largest proper divisor of n.

Original entry on oeis.org

1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 4, 1, 6, 5, 0, 1, 0, 1, 0, 5, 2, 1, 8, 1, 8, 9, 12, 1, 14, 1, 0, 1, 0, 3, 0, 1, 2, 5, 0, 1, 0, 1, 4, 13, 6, 1, 16, 1, 16, 17, 16, 1, 18, 3, 24, 17, 24, 1, 28, 1, 30, 21, 0, 1, 0, 1, 0, 5, 2, 1, 0, 1, 0, 9, 4, 9, 6, 1, 0, 17, 0, 1, 0, 17, 2, 21, 8, 1, 8, 9, 12, 29, 14, 19, 32, 1, 32, 33, 32, 1, 34, 1, 32, 33

Offset: 1

Antti Karttunen, Aug 28 2018

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to binary expansion of n

Cf. A004198, A032742, A060681, A106409, A318508, A318514, A318518.

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318515(n) = bitand(n,A032742(n));

a(n) = A004198(n, A032742(n)).

a(n) = n + A032742(n) - A318514(n) = (n+A032742(n)-A106409(n))/2.

cp's OEIS Frontend

A318458 a(n) = n AND A001065(n), where AND is bitwise-and (A004198) & A001065 = sum of proper divisors.

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A318517 a(n) = A032742(n) XOR n-A032742(n), where XOR is bitwise-xor (A003987) and A032742 = the largest proper divisor of n.

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A318516 a(n) = A032742(n) OR n-A032742(n), where OR is bitwise-or (A003986) and A032742 = the largest proper divisor of n.

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A318515 a(n) = n AND A032742(n), where AND is bitwise-and (A004198) and A032742 = the largest proper divisor of n.

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