A318516 -id:A318516 - cp's OEIS frontend

A318506 a(n) = A032742(n) OR A001065(n)-A032742(n), where OR is bitwise-or (A003986) and A001065 = sum of proper divisors and A032742 = the largest proper divisor of n.

1, 1, 1, 3, 1, 3, 1, 7, 3, 7, 1, 14, 1, 7, 5, 15, 1, 13, 1, 14, 7, 11, 1, 28, 5, 15, 13, 14, 1, 31, 1, 31, 15, 19, 7, 55, 1, 19, 13, 30, 1, 53, 1, 22, 31, 23, 1, 60, 7, 27, 21, 30, 1, 63, 15, 60, 23, 31, 1, 94, 1, 31, 21, 63, 15, 45, 1, 58, 23, 39, 1, 119, 1, 39, 25, 62, 11, 55, 1, 106, 31, 43, 1, 106, 23, 43, 29, 60, 1, 111, 13, 62, 31

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. A001065, A003986, A032742, A318505, A318507, A318508.

Cf. also A318456, A318516.

A001065(n) = (sigma(n)-n);
A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318505(n) = if(1==n,0,A001065(n)-A032742(n));
A318506(n) = bitor(A318505(n),A032742(n));

a(n) = A003986(A032742(n), A318505(n)).

For n > 1, a(n) = A001065(n) - A318508(n).

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).

A318518 a(n) = A032742(n) AND n-A032742(n), where AND is bitwise-and (A004198) and A032742 = the largest proper divisor of n.

Original entry on oeis.org

0, 1, 0, 2, 0, 3, 0, 4, 2, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 6, 11, 0, 12, 4, 13, 0, 14, 0, 15, 0, 16, 2, 17, 4, 18, 0, 19, 8, 20, 0, 21, 0, 22, 14, 23, 0, 24, 2, 25, 0, 26, 0, 27, 8, 28, 2, 29, 0, 30, 0, 31, 0, 32, 4, 33, 0, 34, 6, 35, 0, 36, 0, 37, 16, 38, 2, 39, 0, 40, 18, 41, 0, 42, 0, 43, 24, 44, 0, 45, 12, 46, 30, 47, 0, 48, 0, 49, 0, 50, 0, 51, 0

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, A318515, A318516, A318517.

Cf. also A318508.

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318518(n) = bitand(A032742(n),n-A032742(n));

a(n) = A004198(A032742(n), A060681(n)).

a(n) = n - A318516(n) = (n - A318517(n))/2.

A318514 a(n) = n OR (greatest proper divisor of n).

Original entry on oeis.org

1, 3, 3, 6, 5, 7, 7, 12, 11, 15, 11, 14, 13, 15, 15, 24, 17, 27, 19, 30, 23, 31, 23, 28, 29, 31, 27, 30, 29, 31, 31, 48, 43, 51, 39, 54, 37, 55, 47, 60, 41, 63, 43, 62, 47, 63, 47, 56, 55, 59, 51, 62, 53, 63, 63, 60, 59, 63, 59, 62, 61, 63, 63, 96, 77, 99, 67, 102, 87, 103, 71, 108, 73, 111, 91, 110, 79, 111, 79, 120, 91, 123, 83, 126

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, A106409, A318506, A318515, A318516.

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318514(n) = bitor(n,A032742(n));

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

a(n) = n + A032742(n) - A318515(n).

cp's OEIS Frontend

A318506 a(n) = A032742(n) OR A001065(n)-A032742(n), where OR is bitwise-or (A003986) and A001065 = sum of proper divisors and A032742 = the largest proper divisor of n.

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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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A318518 a(n) = A032742(n) AND n-A032742(n), where AND is bitwise-and (A004198) and A032742 = the largest proper divisor of n.

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A318514 a(n) = n OR (greatest proper divisor of n).

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