cp's OEIS Frontend

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.

A202479 The number of equivalence classes of the set {1,2,...,n} under the equivalence relation x ~ y iff lcm(x,n) = lcm(y,n).

This page as a plain text file.
%I A202479 #21 Apr 23 2020 07:40:59
%S A202479 1,1,2,2,4,3,6,4,6,6,10,6,12,9,9,8,16,9,18,10,14,15,22,10,20,18,18,15,
%T A202479 28,15,30,16,23,24,25,16,36,27,28,19,40,21,42,25,26,33,46,20,42,30,37,
%U A202479 30,52,27,42,28,42,42,58,23,60,45,39,32,50,35,66,40,51
%N A202479 The number of equivalence classes of the set {1,2,...,n} under the equivalence relation x ~ y iff lcm(x,n) = lcm(y,n).
%H A202479 Amiram Eldar, <a href="/A202479/b202479.txt">Table of n, a(n) for n = 1..10000</a>
%H A202479 Hamid Kulosman, <a href="https://www.researchgate.net/publication/265700639_The_number_of_equivalence_classes_of_the_relation_lcmxnlcmyn_on_the_set_12n">The number of equivalence classes of the relation lcm(x,n) = lcm(y,n) on the set {1,2,...,n}</a>, Rad. Mat. 7 (1991), pp. 143-150.
%F A202479 h(n) = symb floor(prod_{i=1..k} (p_i^a_i - p_i^(a_i-1) + 1/p_i), where n=p_1^a_1 * ... * p_k^a_k and the symbol symb symbolizes that first the multiplication of all factors is performed and then floor is assigned to each of the 3^k terms, keeping the sign of the term outside (this symbol is occurring in W. Sierpinski's 1950 monograph Number Theory).
%t A202479 a[n_] := Length @ Union @ Table[LCM[n, i], {i, 1, n}]; Array[a, 100] (* _Amiram Eldar_, Apr 23 2020 *)
%o A202479 (PARI) a(n)=#Set(vector(n,i,lcm(n,i))) \\ _Charles R Greathouse IV_, Dec 19 2011
%K A202479 nonn
%O A202479 1,3
%A A202479 _Hamid Kulosman_, Dec 19 2011