A262066 - OEIS

%I #12 Sep 11 2015 03:36:57

%S 1,2,1,4,9,7,25,8,13,7,17,10,121,27,169,16,29,39,289,12,37,19,41,26,

%T 529,47,19,133,53,34,841,32,61,31,43,93,29,35,73,217,81,63,23,50,21,

%U 43,89,58,2209,75,97,77,101,40,2809,36,109,343,113,74,3481,65,3721

%N a(n) = A017666(A243512(n)).

%C a(n) is the denominator of sigma(m)/m when m is A243512(n), the least integer i such that sigma(i)/i = (k+n)/k for some k.

%H Michel Marcus, <a href="/A262066/b262066.txt">Table of n, a(n) for n = 0..629</a>

%F a(n) = A017665(A243512(n)) - n.

%e For n=2, A243512(2) is 120 with sigma(120)/120=3/1 and 3/1=(2+1)/1 so a(2)=1.

%e For n=3, A243512(3) is 4 with sigma(4)/4=7/4 and 7/4=(4+3)/4 so a(3)=4.

%t f[n_] := Block[{r = DivisorSigma[1, n]/n}, Numerator[r] - Denominator@ r]; Denominator[DivisorSigma[-1, #]] & /@ Table[i = 1; While[f@ i != n, i++]; i, {n, 0, 62}] (* _Michael De Vlieger_, Sep 10 2015 *)

%o (PARI) oksk(n, k) = {my(ab = sigma(k,-1)); numerator(ab) == denominator(ab)+n;}

%o a(n) = {my(k=1); while(!oksk(n, k), k++); denominator(sigma(k,-1));}

%Y Cf. A017665, A017666, A243473, A243512.

%K nonn

%O 0,2

%A _Michel Marcus_, Sep 10 2015