Because a hundred and eleven is three times thirty-seven, it stands behind a family of arithmetical curiosities: six times a hundred and eleven is six hundred and sixty-six, the number of the beast, and the repdigits two hundred and twenty-two through nine hundred and ninety-nine are its multiples. In the modern vocabulary of angel numbers a hundred and eleven, like the other repeated ones, is read as a sign of alignment and new beginnings, a twenty-first-century usage with no older pedigree. The number's genuine interest is its repunit form and the gematria of the spelled-out aleph; the rest is recreational arithmetic or recent invention.
A hundred and eleven factors as 3 x 37 and carries 4 divisors in all. Summing its proper divisors gives only 41, 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.