A247130 a(n) = A272295(m) where m is the n-th integer that is both squarefree and not divisible by 3.

1, 3, -3, -5, 7, 9, -9, -11, 15, -15, -9, 19, 21, -21, -23, 27, -15, -29, 31, 21, -33, -35, 37, 15, -39, -41, 27, 45, -21, -27, 49, 51, -51, -53, 55, 57, -33, -27, -63, -65, 27, 69, -69, -35, 45, 75, -75, -45, 79, 33, -81, -83, 87, -89, 91, 57, -45, -95, 97, 99, -99

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Formula

Sum_((mu(n))*1/a(n)),mu(n)=moebius(n) {n >= 1, n not divisible by 2 or 3}=1 + (-1)*1/(3) + (-1)*1/(-3) + (-1)*1/(-5) + (-1)*1/(7) + (-1)*1/(9) + (-1)*1/(-9) + (-1)*1/(-11) + (-1)*1/(15) + (-1)*1/(-15) + (1)*1/(-9) + (-1)*1/(19)+ (-1)*1/(21) + (-1)*1/(-21) + (-1)*1/(-23) + (-1)*1/(27) + (1)*1/(-15)*... = 1.

Prog

(PARI) {
zv=0.0;
forstep(n=1, 200, 2,
       if(n%3<>0,
           mb=moebius(n);
           if(mb<>0,
              fa=factorint(n);
              dv=fa[, 1]; pl=#dv; ml=fa[, 2];
              g=1;
              for(i=1, pl,
                 ds=dv[i]; v=1;
                 if(ds%4==1, v*=(1+ds)\2, v*=(1-ds)\2);
                 for(k=1, ml[i], g*=v)
               );
               zv+=mb/g;
               print1(g", ")
            )
        )
     );
   print(); print(zv);
}
(PARI) lista(nn) = {forstep (n=1, nn, 2, if (issquarefree(n) && (n % 3), f = factor(n); for (k=1, #f~, if (f[k, 1] == 2, f[k, 1] = 0, if (f[k, 1] % 4 == 1, f[k, 1] = (1+f[k, 1])/2, f[k, 1] = (1-f[k, 1])/2)); ); print1(factorback(f), ", "); ); ); } \\ Michel Marcus, May 02 2016

Crossrefs

Subsequence of A272295.

Sequence in context: A171957 A278166 A293990 * A271974 A050824 A323703

Adjacent sequences: A247127 A247128 A247129 * A247131 A247132 A247133

Keyword

sign

Author

Dimitris Valianatos, Apr 30 2016

Status

approved