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.

A187106 Number of nonempty subsets of {1, 2, ..., n} having pairwise coprime elements.

This page as a plain text file.
%I A187106 #21 Aug 24 2016 21:10:53
%S A187106 1,3,7,11,23,27,55,71,103,115,231,247,495,543,615,727,1455,1519,3039,
%T A187106 3231,3615,3871,7743,7999,11167,11903,14655,15487,30975,31231,62463,
%U A187106 69887,76159,80255,89855,91647,183295,192639,208639,214271,428543
%N A187106 Number of nonempty subsets of {1, 2, ..., n} having pairwise coprime elements.
%H A187106 Alois P. Heinz, <a href="/A187106/b187106.txt">Table of n, a(n) for n = 1..220</a>
%F A187106 a(n) = Sum_{k=1..A036234(n)} A186974(n,k).
%F A187106 a(n) = Sum_{i=1..n} A186973(i).
%F A187106 a(n) = A187262(n,A036234(n)).
%F A187106 a(n) = A084422(n) - 1.
%e A187106 a(4) = 11 because there are 11 nonempty subsets of {1,2,3,4} having pairwise coprime elements: {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {3,4}, {1,2,3}, {1,3,4}.
%o A187106 (PARI) f(n,k=1)=if(n==1, return(2)); if(gcd(k,n)==1, f(n-1,n*k)) + f(n-1,k)
%o A187106 a(n)=f(n)-1 \\ _Charles R Greathouse IV_, Aug 24 2016
%Y A187106 Cf. A036234. Row sums of triangle A186974. Partial sums of A186973. Rightmost elements in rows of triangle A187262.
%Y A187106 Cf. A084422.
%K A187106 nonn
%O A187106 1,2
%A A187106 _Alois P. Heinz_, Mar 06 2011