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

1,4

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

Formula

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

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

Prog

(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));

Crossrefs

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

Cf. also A106409, A318457, A318462, A318517.

Sequence in context: A106800 A308484 A227320 * A055807 A364285 A213060

Adjacent sequences: A318504 A318505 A318506 * A318508 A318509 A318510

Keyword

nonn,base

Author

Antti Karttunen, Aug 28 2018

Status

approved