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A065803 a(n) = (sigma_2(n) mod 2) * (sigma_2(n) mod 5). Residue-product modulo 2 and 5 of sum of square of divisors.

%I A065803 #26 Feb 16 2025 08:32:45
%S A065803 1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
%T A065803 0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
%U A065803 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3
%N A065803 a(n) = (sigma_2(n) mod 2) * (sigma_2(n) mod 5). Residue-product modulo 2 and 5 of sum of square of divisors.
%C A065803 If n is square then sigma_2(n) is divisible by neither 2 nor 5. The product of residues is not always one. E.g., sigma_2(121) = 14673; mod 2 and mod 5 gives 1 and 3 residues. a(n)=3 for n=121, 361, 484, 841, 961 etc..
%C A065803 a(n)=4 for n=43681, 101761, 116281, 174724, 203401, 303601, 346921, ... - _R. J. Mathar_, Apr 02 2011
%D A065803 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A065803 Antti Karttunen, <a href="/A065803/b065803.txt">Table of n, a(n) for n = 1..101761</a> (terms 1..10000 from Charles R Greathouse IV)
%H A065803 Robert Price, <a href="/A065803/a065803.txt">Comments on A065803 concerning Elementary Cellular Automata</a>, Jan 29 2016
%H A065803 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A065803 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A065803 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A065803 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A065803 a(n) = (A001157(n) mod 2) * (A001157(n) mod 5).
%p A065803 A001157 := proc(n) numtheory[sigma][2](n) ; end proc:
%p A065803 A065803 := proc(n) (A001157(n) mod 2)*(A001157(n) mod 5) ; end proc: # _R. J. Mathar_, Apr 02 2011
%t A065803 Array[Mod[#, 2] Mod[#, 5] &@ DivisorSigma[2, #] &, 121] (* _Michael De Vlieger_, Jan 19 2020 *)
%o A065803 (PARI) a(n)=if(issquare(n), sigma(n,2)%5, 0) \\ _Charles R Greathouse IV_, Nov 19 2014
%Y A065803 Cf. A001157, A053866, A000290.
%K A065803 easy,nonn
%O A065803 1,121
%A A065803 _Labos Elemer_, Nov 21 2001
%E A065803 Data section extended up to a(121) by _Antti Karttunen_, Jan 18 2020