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A284570 a(n) = A000005((n+1)^2) - A000005(n^2).

%I A284570 #20 Jul 21 2023 20:09:01
%S A284570 2,0,2,-2,6,-6,4,-2,4,-6,12,-12,6,0,0,-6,12,-12,12,-6,0,-6,18,-16,4,
%T A284570 -2,8,-12,24,-24,8,-2,0,0,16,-22,6,0,12,-18,24,-24,12,0,-6,-6,24,-22,
%U A284570 10,-6,6,-12,18,-12,12,-12,0,-6,42,-42,6,6,-2,-4,18,-24,12,-6,18,-24,32,-32,6,6,0,-6,18,-24,24,-18,0,-6,42,-36,0,0,12,-18,42,-36,6,-6
%N A284570 a(n) = A000005((n+1)^2) - A000005(n^2).
%H A284570 Antti Karttunen, <a href="/A284570/b284570.txt">Table of n, a(n) for n = 1..10000</a>
%F A284570 a(n) = A000005((n+1)^2) - A000005(n^2).
%F A284570 a(n) = A048691(n+1) - A048691(n). - _Michel Marcus_, Apr 15 2017
%t A284570 Table[DivisorSigma[0, (n + 1)^2] - DivisorSigma[0, n^2], {n, 100}] (* _Indranil Ghosh_, Apr 15 2017 *)
%t A284570 Differences[DivisorSigma[0,Range[100]^2]] (* _Harvey P. Dale_, Jul 21 2023 *)
%o A284570 (PARI) A284570(n) = numdiv((n+1)^2)-numdiv(n^2);
%o A284570 (Scheme) (define (A284570 n) (- (A000005 (A000290 (+ 1 n))) (A000005 (* n n))))
%o A284570 (Python)
%o A284570 from sympy import divisor_count as D
%o A284570 print([D((n + 1)**2) - D(n**2) for n in range(1, 101)]) # _Indranil Ghosh_, Apr 15 2017
%Y A284570 Cf. A000005, A000290, A048691, A276553 (positions of zeros).
%K A284570 sign
%O A284570 1,1
%A A284570 _Antti Karttunen_, Apr 15 2017