cp's OEIS Frontend

A231122 Numbers k >= 0 such that 2^k is number of ways to write n as n = x*y, where x, y = squarefree numbers, 1 <= x <= n, 1 <= y <= n, or -1 if no such k exists.

%I A231122 #22 Nov 05 2013 06:31:09
%S A231122 0,0,0,0,0,1,0,-1,0,1,0,0,0,1,1,-1,0,0,0,0,1,1,0,-1,0,1,-1,0,0,2,0,-1,
%T A231122 1,1,1,0,0,1,1,-1,0,2,0,0,0,1,0,-1,0,0,1,0,0,-1,1,-1,1,1,0,1,0,1,0,-1,
%U A231122 1,2,0,0,1,2,0,-1,0,1,0,0,1,2,0,-1,-1,1,0,1,1
%N A231122 Numbers k >= 0 such that 2^k is number of ways to write n as n = x*y, where x, y = squarefree numbers, 1 <= x <= n, 1 <= y <= n, or -1 if no such k exists.
%H A231122 Charles R Greathouse IV, <a href="/A231122/b231122.txt">Table of n, a(n) for n = 1..10000</a>
%e A231122 1(1*1), 2(1*2), 3(1*3), 4(2*2), 5(1*5), 6(1*6, 2*3), 7(1*7), 8(-), 9(3*3), 10(1*10, 2*5), 11(1*11), 12(2*6), 13(1*13), 14(1*14, 2*7), 15(1*15, 3*5), 16(-), 17(1*17), 18(3*6), 19(1*19), 20(2*10), 21(1*21, 3*7), 22(1*22, 2*11), 23(1*23), 24(-), 25(5*5), 26(1*26, 2*13), 27(-).
%o A231122 (PARI) a(n)=if(n==1,return(0)); my(f=factor(n)[,2]); if(vecmax(f)>2, return(-1)); max(sum(i=1,#f,2-f[i])-1, 0) \\ _Charles R Greathouse IV_, Nov 04 2013
%Y A231122 Cf. A046099(k<0), A130091(k<=0), A004709(k>=0), A230843(k=0), (A006881 U A085987 U ...)(k=1).
%K A231122 sign
%O A231122 1,30
%A A231122 _Gerasimov Sergey_, Nov 04 2013
%E A231122 a(80) corrected by _Charles R Greathouse IV_, Nov 04 2013