A292307 - OEIS

%I #21 Sep 19 2017 06:48:14

%S 15,5,26565,7,315,11,15,11,79695,13,15,17,75,17,56815934175,22,45,23,

%T 75,23,7767045,55,45,29,189,38,5005,31,75,37,45,44,116025,37,3795,43,

%U 135,41,345345,43,135,47,195,110,170447802525,110,118,53,105,53,451605,76

%N a(n) is the smallest k > n such that psi(k) is the arithmetic mean of psi(k - n) and psi(k + n), or 0 if no such k exists.

%C It seems that a(n) tends to be quite large when n is an odd multiple of 15. We have a(15) = 56815934175, a(45) = 170447802525, a(75) = 284079670875, and a(105) > 10^12. - _Giovanni Resta_, Sep 15 2017

%e For the equation psi(k - 3) + psi(k + 3) = 2*psi(k), the smallest solution is k = 26565.

%o (PARI) a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1));

%o a(n) = {my(k=n+1); while (a001615(k-n)+a001615(k+n) != 2*a001615(k), k++); k; } \\ after _Charles R Greathouse IV_ at A001615

%Y Cf. A001615.

%K nonn

%O 1,1

%A _Altug Alkan_, Sep 14 2017

%E a(15)-a(52) from _Giovanni Resta_, Sep 15 2017