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A176035 Difference between product of two distinct primes and previous perfect square.

%I A176035 #10 Aug 25 2025 11:42:34
%S A176035 2,1,5,6,5,6,1,8,9,10,2,3,10,2,6,8,9,13,1,5,10,13,1,4,5,6,10,12,13,14,
%T A176035 6,11,15,18,19,1,2,8,12,13,20,21,22,1,2,11,14,15,17,22,8,9,14,16,18,
%U A176035 25,5,6,7,9,10,13,17,18,19,21,22,23,25,1,10,12,22,24,28,29,3,6,9,11,18,22,31
%N A176035 Difference between product of two distinct primes and previous perfect square.
%C A176035 6-4=2, 10-9=1, 14-9=5, 15-9=6, 21-16=5,..
%H A176035 G. C. Greubel, <a href="/A176035/b176035.txt">Table of n, a(n) for n = 1..5000</a>
%F A176035 a(n) = A053186(A006881(n)). - _R. J. Mathar_, Aug 25 2025
%t A176035 A006881=Sort@Flatten@Table[Prime[m]*Prime[n], {n, 2, 150}, {m, n-1}];
%t A176035 Table[A006881[[n]]-Floor[Sqrt[A006881[[n]]]]^2, {n, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 02 2011 *)
%o A176035 (Magma)
%o A176035 A006881:= [n: n in [1..1000] | EulerPhi(n) + DivisorSigma(1, n) eq 2*(n+1)];
%o A176035 [A006881[n] - Floor(Sqrt(A006881[n]))^2: n in [1..100]]; // _G. C. Greubel_, Oct 26 2022
%o A176035 (SageMath)
%o A176035 A006881=[n for n in (1..750) if euler_phi(n) + sigma(n,1) == 2*n+2]
%o A176035 [A006881[n] - isqrt(A006881[n])^2 for n in range(101)] # _G. C. Greubel_, Oct 26 2022
%Y A176035 Cf. A006881, A056892, A106044, A176032, A176033, A176034
%K A176035 nonn,changed
%O A176035 1,1
%A A176035 _Vladimir Joseph Stephan Orlovsky_, Apr 06 2010