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a(n) = (Sum_{d|n} sigma(d)) mod sigma(n).
4

%I #29 Dec 14 2024 10:26:05

%S 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 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 112,19,114,25,34,1,49,1,36,58,120,21,116,1,83,29,108

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

%H Antti Karttunen, <a href="/A319296/b319296.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A007429(n) mod A000203(n).

%F a(A221219(n)) = 0.

%F a(A000040(n)) = 1; the only composite number < 2*10^6 with a(n) = 1 is 636.

%F a(n) = n only for numbers 4, 10 and 96 < 3000000.

%e For n = 4; a(4) = (sigma(1) + sigma(2) + sigma(4)) mod sigma(4) = (1+3+7) mod 7 = 11 mod 7 = 4.

%t Table[Mod[Sum[DivisorSigma[1, d], {d, Divisors[n]}], DivisorSigma[1, n]], {n, 1, 100}] (* _Vaclav Kotesovec_, Sep 26 2018 *)

%o (Magma) [&+[SumOfDivisors(d): d in Divisors(n)] mod SumOfDivisors(n): n in [1..1000]];

%o (PARI) A319296(n) = (sumdiv(n,d,sigma(d))%sigma(n)); \\ _Antti Karttunen_, Sep 16 2018

%Y Cf. A000040, A000203, A007429, A221219.

%K nonn

%O 1,4

%A _Jaroslav Krizek_, Sep 16 2018