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A319296 a(n) = (Sum_{d|n} sigma(d)) mod sigma(n).

%I A319296 #29 Dec 14 2024 10:26:05
%S A319296 0,1,1,4,1,8,1,11,5,10,1,27,1,12,11,26,1,33,1,35,13,16,1,10,7,18,18,
%T A319296 43,1,68,1,57,17,22,15,16,1,24,19,2,1,84,1,59,48,28,1,37,9,59,23,67,1,
%U A319296 112,19,114,25,34,1,49,1,36,58,120,21,116,1,83,29,108
%N A319296 a(n) = (Sum_{d|n} sigma(d)) mod sigma(n).
%H A319296 Antti Karttunen, <a href="/A319296/b319296.txt">Table of n, a(n) for n = 1..65537</a>
%F A319296 a(n) = A007429(n) mod A000203(n).
%F A319296 a(A221219(n)) = 0.
%F A319296 a(A000040(n)) = 1; the only composite number < 2*10^6 with a(n) = 1 is 636.
%F A319296 a(n) = n only for numbers 4, 10 and 96 < 3000000.
%e A319296 For n = 4; a(4) = (sigma(1) + sigma(2) + sigma(4)) mod sigma(4) = (1+3+7) mod 7 = 11 mod 7 = 4.
%t A319296 Table[Mod[Sum[DivisorSigma[1, d], {d, Divisors[n]}], DivisorSigma[1, n]], {n, 1, 100}] (* _Vaclav Kotesovec_, Sep 26 2018 *)
%o A319296 (Magma) [&+[SumOfDivisors(d): d in Divisors(n)] mod  SumOfDivisors(n): n in [1..1000]];
%o A319296 (PARI) A319296(n) = (sumdiv(n,d,sigma(d))%sigma(n)); \\ _Antti Karttunen_, Sep 16 2018
%Y A319296 Cf. A000040, A000203, A007429, A221219.
%K A319296 nonn
%O A319296 1,4
%A A319296 _Jaroslav Krizek_, Sep 16 2018