A053867 Parity of sum of divisors of n less than n.

0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1

Offset

1,1

Comments

Partial sums up to n is about n/2. - David A. Corneth, Oct 20 2017

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for characteristic functions

Index entries for sequences related to sums of divisors

Formula

a(n) = A001065(n) mod 2.

a(2n+1) = 1 - A010052(2n+1); a(4n + 2) = 1 - a(2n + 1); a(4n) = a(2n). - David A. Corneth, Oct 20 2017

Example

a(9) = 0 because sum of proper divisors of 9 is 1 + 3 = 4 which is an even number.
From David A. Corneth, Oct 20 2017: (Start)
a(25) = 0 because 25 is an odd square. Therefore, a(2*25) = a(50) = 1 - a(25) = 1 and a(100) = a(2*50) = 1.
a(27) = 1 because 17 isn't an odd square. Therefore, a(2*27) = a(54) = 1-a(27) = 0 and a(108) = a(2*54) = 0. (End)

Prog

(PARI) A053867(n) = ((sigma(n)-n)%2); \\ Antti Karttunen, Oct 20 2017
(PARI) first(n) = my(res = vector(n, i, i%2)); forstep(i=1, sqrtint(n), 2, for(j=0, logint(n\i^2, 2), c = i^2 << j; res[c] = 1 - res[c])); res \\ David A. Corneth, Oct 20 2017

Crossrefs

Cf. A000005, A000265, A001065, A010052, A053866.

Sequence in context: A324828 A332823 A354817 * A189727 A361113 A268411

Adjacent sequences: A053864 A053865 A053866 * A053868 A053869 A053870

Keyword

nonn,easy

Author

Henry Bottomley, Mar 29 2000

Extensions

More terms from James A. Sellers, Apr 08 2000

Status

approved