

A292307


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.


0



15, 5, 26565, 7, 315, 11, 15, 11, 79695, 13, 15, 17, 75, 17, 56815934175, 22, 45, 23, 75, 23, 7767045, 55, 45, 29, 189, 38, 5005, 31, 75, 37, 45, 44, 116025, 37, 3795, 43, 135, 41, 345345, 43, 135, 47, 195, 110, 170447802525, 110, 118, 53, 105, 53, 451605, 76
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OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..52.


EXAMPLE

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


PROG

(PARI) a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]1));
a(n) = {my(k=n+1); while (a001615(kn)+a001615(k+n) != 2*a001615(k), k++); k; } \\ after Charles R Greathouse IV at A001615


CROSSREFS

Cf. A001615.
Sequence in context: A241361 A249996 A128251 * A064107 A116907 A277384
Adjacent sequences: A292304 A292305 A292306 * A292308 A292309 A292310


KEYWORD

nonn


AUTHOR

Altug Alkan, Sep 14 2017


EXTENSIONS

a(15)a(52) from Giovanni Resta, Sep 15 2017


STATUS

approved



