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 A053867 Parity of sum of divisors of n less than n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 22 08:14 EDT 2024. Contains 374481 sequences. (Running on oeis4.)