A318507 a(n) = A032742(n) XOR A001065(n)-A032742(n), where XOR is bitwise-or (A003987) and A001065 = sum of proper divisors and A032742 = the largest proper divisor of n.

1, 1, 1, 3, 1, 0, 1, 7, 2, 6, 1, 12, 1, 4, 1, 15, 1, 5, 1, 6, 3, 8, 1, 20, 4, 14, 13, 0, 1, 20, 1, 31, 15, 18, 1, 55, 1, 16, 9, 10, 1, 52, 1, 4, 29, 20, 1, 44, 6, 11, 21, 14, 1, 60, 13, 56, 23, 30, 1, 80, 1, 28, 1, 63, 11, 12, 1, 58, 19, 4, 1, 115, 1, 38, 1, 60, 3, 20, 1, 106, 22, 42, 1, 72, 23, 40, 25, 28, 1, 78, 5, 48, 27, 44, 21, 92, 1

Offset: 1

Author

Antti Karttunen, Aug 28 2018

Keywords

• nonn
• base

Comments

Note that here zeros occur only on even perfect numbers (even terms of A000396), in contrast to A318457, which would be zero also for any hypothetical odd perfect number. - Antti Karttunen, Aug 29 2018

Links

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

Crossrefs

Cf. A000396, A001065, A003987, A032742, A318505, A318506, A318508.

Cf. also A106409, A318457, A318462, A318517.

Programs

PARI

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));
A318507(n) = bitxor(A318505(n),A032742(n));

Formula

a(n) = A003987(A032742(n), A318505(n)).

For n > 1, a(n) = A001065(n) - 2*A318508(n).