This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A180772 #20 Apr 28 2023 08:20:40 %S A180772 0,0,0,1,0,2,0,3,3,4,0,9,0,6,8,10,0,15,0,17,12,10,0,27,10,12,15,25,0, %T A180772 38,0,26,20,16,24,51,0,18,24,51,0,56,0,41,51,22,0,74,21,50,32,49,0,69, %U A180772 40,75,36,28,0,121,0,30,75,68,48,92,0,65,44,106,0,141,0,36,90,73,60,110,0,138 %N A180772 Number of distinct solutions to the congruence x(1)*x(2) == 0 (mod n), with x() only in 1..n-1. %C A180772 Also, number of ordered pairs (a, b) with 0 < a <= b such that a*b = c*n + d and c = d where 0 < a, b, c, d < n. - _Naohiro Nomoto_, Oct 02 2021 %H A180772 R. H. Hardin, <a href="/A180772/b180772.txt">Table of n, a(n) for n=1..10000</a> %F A180772 a(n) = A174088(n) - n = ( A018804(n) + A000188(n) )/2 - n. %e A180772 The a(12)=9 solutions for product of a single 1..11 pair == 0 (mod 12) are 2*6, 3*4, 3*8, 4*6, 4*9, 6*6, 6*8, 6*10, and 8*9. %t A180772 f1[p_, e_] := (e*(p - 1)/p + 1)*p^e; f2[p_, e_] := p^Floor[e/2]; a[n_] := (Times @@ f1 @@@ (fct = FactorInteger[n]) + Times @@ f2 @@@ fct)/2 - n; Array[a, 100] (* _Amiram Eldar_, Apr 28 2023 *) %Y A180772 Column 1 of A180782. %Y A180772 Cf. A000188, A018804, A174088. %K A180772 nonn %O A180772 1,6 %A A180772 _R. H. Hardin_, formula from _Max Alekseyev_ in the Sequence Fans Mailing List, Sep 20 2010