cp's OEIS Frontend

A317443 a(n) = number of k with 1 <= k <= n-1 such that a(k) + a(n-k) is not squarefree.

%I A317443 #12 Aug 02 2018 11:54:16
%S A317443 0,1,0,2,0,3,0,7,0,7,0,10,0,9,2,8,4,9,8,10,8,11,10,17,8,13,12,15,4,19,
%T A317443 4,25,6,17,8,25,12,19,10,27,10,23,14,22,16,25,16,26,12,21,16,22,14,31,
%U A317443 16,40,14,29,20,32,14,27,22,35,24,33,24,32,28,25,18
%N A317443 a(n) = number of k with 1 <= k <= n-1 such that a(k) + a(n-k) is not squarefree.
%C A317443 We consider that 0 is not squarefree.
%C A317443 The scatterplot of the sequence has stripes linked to the 2-adic valuation of n.
%C A317443 See A317420 for similar sequences.
%H A317443 Rémy Sigrist, <a href="/A317443/b317443.txt">Table of n, a(n) for n = 1..10000</a>
%H A317443 Rémy Sigrist, <a href="/A317443/a317443.png">Colored scatterplot of the first 1000000 terms</a> (where the color is function of A007814(n))
%e A317443 For n = 4:
%e A317443 - a(1) + a(3) = 0 + 0 = 0 is not squarefree,
%e A317443 - a(2) + a(2) = 1 + 1 = 2 is squarefree,
%e A317443 - a(3) + a(1) = 0 + 0 = 0 is not squarefree,
%e A317443 - hence a(4) = 2.
%o A317443 (PARI) a = vector(71); for (n=1, #a, a[n] = sum(k=1, n-1, !issquarefree(a[k]+a[n-k])); print1 (a[n] ", "))
%Y A317443 Cf. A007814, A013929, A317420.
%K A317443 nonn
%O A317443 1,4
%A A317443 _Rémy Sigrist_, Jul 28 2018