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A280987 {Concatenation n, n-1, n-2, ...3,2,1} mod sigma(n).

%I A280987 #13 Aug 08 2025 15:04:01
%S A280987 0,0,1,2,3,9,1,6,4,1,9,21,1,9,9,16,9,24,1,33,17,1,9,21,0,9,1,41,21,33,
%T A280987 17,6,33,19,33,25,25,21,1,1,33,81,17,21,45,1,33,85,49,69,57,77,27,81,
%U A280987 1,81,1,1,21,57,59,81,33,60,21,33,45,51,81,1,9,66,41,9,97,1,81,81,1,57,117,73,33,145
%N A280987 {Concatenation n, n-1, n-2, ...3,2,1} mod sigma(n).
%H A280987 Indranil Ghosh, <a href="/A280987/b280987.txt">Table of n, a(n) for n = 1..10000</a>
%F A280987 a(n) = A000422(n) mod A000203(n).
%e A280987 For n = 11, A000422(n) mod sigma(n) = 1110987654321 mod 12 = 9. S0 a(11) = 9.
%t A280987 Table[Mod[FromDigits[Flatten[IntegerDigits/@Range[n,1,-1]]],DivisorSigma[ 1,n]],{n,90}] (* _Harvey P. Dale_, Jul 01 2020 *)
%o A280987 (Python)
%o A280987 def sigma(n):
%o A280987     s=0
%o A280987     for i in range(1,n+1):
%o A280987         if n%i==0:
%o A280987             s+=i
%o A280987     return s
%o A280987 def C(n):
%o A280987     s=""
%o A280987     for i in range(n,0,-1):
%o A280987         s+=str(i)
%o A280987     return int(s)
%o A280987 for i in range(1,101):
%o A280987     print(i, C(i)%sigma(i))
%o A280987 (Python)
%o A280987 from sympy import divisor_sigma
%o A280987 def A280987(n): return int(''.join(map(str, range(n, 0, -1)))) % divisor_sigma(n) # _David Radcliffe_, Aug 08 2025
%Y A280987 Cf. A000203, A000422, A114795.
%K A280987 nonn,base
%O A280987 1,4
%A A280987 _Indranil Ghosh_, Jan 12 2017