Modern numerology reduces sixty-one to seven and reads it as a number of introspection and analysis, the seven reached through a six of harmony and a one of initiative. Apart from the gematria of ani and this reductive reading, sixty-one carries no traditional symbolism. Its honest description is a prime whose one point of interest is the Hebrew word for I, a small but genuine thread in the Kabbalistic arithmetic of the self.
Nicomachus's own arithmetic sorted whole numbers into deficient, perfect and abundant by comparing them with the sum of their own divisors, a genuinely ancient classification that has nothing to do with the letter charts later numerologists built; the modern system that assigns meaning to digit sums is a distinct, twentieth-century construction that happens to borrow the Pythagorean name.
None of this genealogy is hidden by the numerologists themselves: Balliett, Campbell and Jordan each wrote openly as originators and systematisers rather than as transmitters of a secret ancient science, and the chain from Balliett's 1908 book through Campbell's 1931 manual to Jordan's 1965 standardisation is well documented in the numerology literature's own bibliographies.
Where the Chaldean chart and the Balliett-descended chart assign different values to the same letters, a name totalling one figure in one system need not total the same figure in the other, since the two rest on unrelated letter-value tables rather than on a shared inheritance from any single ancient source.