Sixty-five is the magic constant of the five-by-five square, the grid in which every row, column and diagonal sums to sixty-five, which the Renaissance tradition of planetary squares assigned to Mars. As a number that also reduces, through eleven, toward the intuitive, sixty-five gathers a modest cluster of associations, the name Adonai, the Mars square, but little narrative lore. Its firmest content is the gematria of the spoken Name, one of the anchors, with twenty-six, of the Kabbalistic reading of the divine names.
Sixty-five factors as 5 x 13 and carries 4 divisors in all. Summing its proper divisors gives only 19, short of the number itself, which places it among the deficient numbers in the same classical scheme.
The genuine Pythagorean number philosophy that this modern chart borrows its name from left no writings of its own: Pythagoras and his early followers taught only by mouth, and what survives of their number theory comes instead through Nicomachus of Gerasa, whose Introduction to Arithmetic of the first century CE became the standard authority for a thousand years, and through Iamblichus, who drew on Nicomachus two centuries later; neither wrote anything resembling a name-and-birthdate numerology.